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by Professor Barry Paton Dalhousie University
March 1998 Edition Part Number 321948A-01
Fundamentals of Digital Electronics
Copyright Copyright © 1998 by National Instruments Corporation, 6504 Bridge Point Parkway, Austin, Texas 78730-5039. Universities, colleges, and other educational institutions may reproduce all or part of this publication for educational use. For all other uses, this publication may not be reproduced or transmitted in any form, electronic or mechanical, including photocopying, recording, storing in an information retrieval system, or translating, in whole or in part, without the prior written consent of National Instruments Corporation. Trademarks LabVIEW™ and The Software is the Instrument™ are trademarks of National Instruments Corporation. Product and company names listed are trademarks or trade names of their respective companies.
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Introduction Lab 1 Gates
The AND Gate...............................................................................................1-1 The OR and XOR Gates ................................................................................1-2 Negation.........................................................................................................1-2 The NAND, NOR, and NXOR Gates............................................................1-2 Building Gates from Other Gates ..................................................................1-3 Gates with More than Two Inputs .................................................................1-4 Masking .........................................................................................................1-5 Application: Data Selector.............................................................................1-6 Name that Gate ..............................................................................................1-6 Lab 1 Library VIs ..........................................................................................1-6
Lab 2 Encoders and Decoders
The Die ..........................................................................................................2-2 Modulo 6 Counter..........................................................................................2-3 Encode ...........................................................................................................2-4 Virtual Dice ...................................................................................................2-5 Lab 2 Library VIs ..........................................................................................2-6
Lab 3 Binary Addition
Adder Expansion (Half Adder, Full Adders).................................................3-3 Binary Coded Decimal (BCD).......................................................................3-5 LabVIEW Challenge .....................................................................................3-6 Lab 3 Library VIs ..........................................................................................3-6
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Fundamentals of Digital Electronics
Lab 4 Memory: The D-Latch
Shift Registers................................................................................................4-2 LabVIEW Challenge: The Bucket Brigade ...................................................4-4 Ring Counters ................................................................................................4-4 Lab 4 Library VIs ..........................................................................................4-5
Lab 5 Pseudo-Random Number Generators
A 6-Bit Pseudo-Random Number Generator.................................................5-1 An 8-Bit Pseudo-Random Sequencer ............................................................5-2 8-Bit Pseudo-Random Number Generator.....................................................5-5 Encryption of Digital Data.............................................................................5-6 Lab 5 Library VIs ..........................................................................................5-7
Lab 6 JK Master-Slave Flip-Flop
Binary Counters (1-Bit, 2-Bit, and 4-Bit) ......................................................6-3 8-Bit Binary Counter (with and without Reset).............................................6-5 Summary ........................................................................................................6-5 Lab 6 Library VIs ..........................................................................................6-6
Lab 7 Digital-to-Analog Converter
What is a DAC? .............................................................................................7-1 ALU Simulator ..............................................................................................7-3 Simulating a Real DAC Chip.........................................................................7-4 Waveform Generators....................................................................................7-5 Special DACs.................................................................................................7-6 Lissajous Figures ...........................................................................................7-7 Lab 7 Library VIs ..........................................................................................7-8
Lab 8 Analog-to-Digital Converters, Part I
Purpose of the Analog-to-Digital Converter..................................................8-1 The Ramp ADC .............................................................................................8-2 Tracking ADC................................................................................................8-4 Lab 8 Library VIs ..........................................................................................8-6
Lab 9 Analog-to-Digital Converters, Part II
SAR Simulation .............................................................................................9-3 Summary ........................................................................................................9-4 Lab 9 Library VIs ..........................................................................................9-4
Fundamentals of Digital Electronics
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..12-3 Addition ......................................................Contents Lab 10 Seven-Segment Digital Displays Seven-Segment Display ....12-4 Binary Counter.......................................................................................................................................................................................................................................................................................................................................................................10-5 Lab 11 Serial Communications Serial Transmitter ............................................................................................................................................................12-5 Lab 12 Library VIs .............................11-2 Voltage to Serial Transmitter..........................................................11-4 Lab 11 Library VIs ...........................................11-5 Lab 12 Central Processing Unit Operation of the Arithmetic and Logic Unit......................................................................................................12-6 © National Instruments Corporation v Fundamentals of Digital Electronics .............12-2 The Accumulator .......................10-1 Lab 10 Library VIs .......
Labs 2. make LabVIEW an excellent tool to visualize and demonstrate many of the fundamental concepts of digital electronics. binary addition. you can enhance simulations presented in the text by using a National Instruments DAQ board to interact with the real world through LabVIEW digital I/O. in tutorial sessions as collaborative studies. digital encryption. analog out. seven-segment displays. ADCs. ring counters. D-latches.Introduction Digital electronics is one of the fundamental courses found in all electrical engineering and most science programs. This manual includes a complete set of LabVIEW VIs. The order of the labs follows most electronic textbooks. This manual is designed as a teaching resource to be used in the classroom as demonstrations. Many of the VIs are suitable for both classroom demonstration and laboratory exploration. which in turn are built from fundamental gates. The first six labs cover the fundamental circuits of gates. and the CPU. serial communication. 5. or in the laboratory as interactive exercises. These labs could be presented as challenging problems in a tutorial setting or in a workshop environment. the CPU operation is dependent on the concept of registers and two input operations. and 12 are application oriented and are designed to demonstrate encoding schemes. The great variety of LabVIEW Boolean and numeric controls/indicators. These are best done in the context of a digital electronics lab. The labs can also be grouped to demonstrate special relationships of advanced devices on certain basic gates. and serial VIs. encoders. The text is also included on the CD so that you can customize the material. In each case. The second set of six labs cover advanced topics such as DACs. comparing the LabVIEW simulations with real integrated circuits. together with the wealth of programming structures and functions. and the operation of a CPU. © National Instruments Corporation I-1 Fundamentals of Digital Electronics . For example. The inherent modularity of LabVIEW is exploited in the same way that complex digital integrated circuits are built from circuits of less complexity. and JK flip-flops. analog in.
XOR.Lab 1 Gates Gates are the fundamental building blocks of digital logic circuitry. For the AND gate. a vast array of gating functions can be created. Truth Table for AND Gate A 0 0 1 1 B 0 1 0 1 Q=A AND B 0 0 0 1 © National Instruments Corporation 1-1 Fundamentals of Digital Electronics . The AND gate output is listed in the right column. these are listed in the left and middle columns. B=0. the on state is often represented by a 1 and the off state by a 0. B=1." In digital electronics. The AND Gate A basic AND gate consists of two inputs and an output. If the two inputs are A and B. The relationship between the input signals and the output signals is often summarized in a truth table. B=1. These devices function by "opening" or "closing" to admit or reject the passage of a logical signal. In the following truth table. A=0. the output (often called Q) is "on" only if both A and B are also "on. A=1. and A=1. there are four possible combinations of input states: A=0. Table 1-1. which is a tabulation of all possible inputs and the resulting outputs. B=0. From only a handful of basic gate types (AND. and NOT). OR.
Lab 1 Gates
In LabVIEW, you can specify a digital logic input by toggling a Boolean switch; a Boolean LED indicator can indicate an output. Because the AND gate is provided as a basic built-in LabVIEW function, you can easily wire two switches to the gate inputs and an indicator LED to the output to produce a simple VI that demonstrates the AND gate.
Figure 1-1. LabVIEW AND Function Wired to I/O Terminal Boxes
Run AND gate.vi from the Chap 1.llb VI library. Push the two input buttons and note how the output indicator changes. Verify the above truth table.
The OR and XOR Gates
The OR gate is also a two-input, single-output gate. Unlike the AND gate, the output is 1 when one input, or the other, or both are 1. The OR gate output is 0 only when both inputs are 0.
Figure 1-2. Digital Symbols for the OR and XOR Gates
A related gate is the XOR, or eXclusive OR gate, in which the output is 1 when one, and only one, of the inputs is 1. In other words, the XOR output is 1 if the inputs are different.
Figure 1-3. The NOT Gate
An even simpler gate is the NOT gate. It has only one input and one output. The output is always the opposite (or negation) of the input.
The NAND, NOR, and NXOR Gates
Negation is quite useful. In addition to the three two-input gates already discussed (AND, OR, and XOR), three more are commonly available. These are identical to AND, OR, and XOR, except that the gate output has been
Fundamentals of Digital Electronics
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Lab 1 Gates
negated. These gates are called the NAND ("not AND"), NOR ("not OR"), and NXOR ("not exclusive OR") gates. Their symbols are just the symbols of the unnegated gate with a small circle drawn at the output:
Figure 1-4. Negated AND, OR, and XOR Gates
Run Truth table.vi. Choose a gate and try all combinations of A and B to complete the following truth tables.
Table 1-2. Truth Tables for the Digital Logic Basic Gates
Building Gates from Other Gates
Given a handful of NAND gates, you can reproduce all other basic logic gates. For example, you can form the NOT gate by connecting both NAND input terminals to the same input:
Figure 1-5. NOT Gate Built from a NAND Gate
Similarly, you can easily build an AND gate from two NAND gates:
Figure 1-6. AND Gate from Two NAND Gates
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Fundamentals of Digital Electronics
Lab 1 Gates
An OR requires three NAND gates:
Figure 1-7. OR Gate from Three NAND Gates
Construct a VI that demonstrates that an XOR gate can be constructed from four NAND gates. For reference, see XOR from NAND.vi in the Lab 1 VI library.
Gates with More than Two Inputs
Although LabVIEW includes all the basic two-input gates, you may require more inputs. For example, the AND truth table above can be generalized to three inputs:
Table 1-3. Truth Table for a Three-Point Input AND Gate
From a pair of two-input AND gates, you can easily build a VI that implements the three-input AND:
Figure 1-8. LabVIEW Program for a Three-Input AND Gate
Open the VI called 3 AND.vi and notice the socket and icon, making this VI a full-fledged subVI.
Fundamentals of Digital Electronics
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Lab 1 Gates
As a simple application of how these basic logic gates can be combined, consider the concept of masking. To illustrate this concept, below is the AND truth table with relabeled column headings.
Table 1-4. Truth Table for AND Gate with One Input as a Mask
Mask 0 0 1 1
Effect A is blocked Gate is "closed"
0 0 A is unchanged 1 Gate is "open"
The truth table makes the point that the AND gate can be used as an electronic switch. This point is easily demonstrated in LabVIEW:
Figure 1-9. AND Gate Used as an Electronic Switch
Load and run E-switch.vi to observe the electronic switch in action. You can view the truth tables of other gates from a masking point of view as well. In the following table, reset means "forced to 0" while set means "forced to 1":
Table 1-5. Truth Table for AND, OR and XOR Gates with One Input as a Mask
Mask 0
AND A is reset
A is unchanged A is unchanged
0 1 A is unchanged 1 A is set A is inverted
In summary, there are three useful functions here. To set a state, use OR with a mask of 1. To reset a state, use AND with a mask of 0. To invert a state, use XOR with a mask of 1.
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Fundamentals of Digital Electronics
OR.vi (subVI used in Data select.vi 3 AND. test your skills with the Name that gate VI. called Select.vi) Name that gate. XOR. LabVIEW's Version of a Digital Data Selector Name that Gate The gates in this section form the foundation of much of digital electronics.vi (data selector using basic logic gates) Data select2. NOR.Lab 1 Gates Application: Data Selector Another simple application of basic gates is the data selector. Thus.vi (for AND. As a review. in which a single digital input selects one of two digital streams: Figure 1-10. NAND. to emulate this operation.vi (data selector using the LabVIEW Select function) Oscillator. Lab 1 Library VIs (Listed in the Order Presented) • • • • • • • • • • AND gate.vi (three-input AND operation) Masking.vi (test your knowledge) Fundamentals of Digital Electronics 1-6 © National Instruments Corporation . A complete familiarity with the truth tables is extremely useful.vi (two-input AND operation) Truth table.vi (electronic switch) Data select.vi (demonstration) E-switch. you could rewire the above as: Figure 1-11. A Digital Data Selector Built with Basic Gates LabVIEW includes a built-in function. and NXOR) XOR from NAND.
switch position 7 might be encoded as 0111. © National Instruments Corporation 2-1 Fundamentals of Digital Electronics . They can be thought of as seven lights arranged in an "H" pattern: Figure 2-2. representing the numbers 1-6. from binary codes into output codes. Consider a rotary switch with 10 positions used to input the numbers 0 through 9. Consider the case of a single die. Each switch position is to be encoded by a unique binary sequence. On each of its six sides. you can create any of the six patterns on the face of a die. Figure 2-1. Dot Arrangement Used in Dice Codes By turning on the appropriate lights. The Six Sides of a Die These patterns are traditional. For example.Lab 2 Encoders and Decoders An encoder converts an input device state into a binary representation of ones or zeros. A decoder performs the opposite conversion. one of the following patterns appears.
Table 2-1. the LED terminals are wired to display the four unique patterns A. Base pattern C is found in the numbers 4. B. place seven LED indicators in the "H" pattern on the front panel. LabVIEW Front Panel for Virtual Die Display Fundamentals of Digital Electronics 2-2 © National Instruments Corporation . Pattern D is used only when representing 6.Lab 2 Encoders and Decoders On closer inspection. Base States Used for Each Die Number Die Face 1 2 3 4 5 6 A √ B C D √ √ √ √ √ √ √ √ √ √ √ The base pattern A is used by all odd numbers (1. the meaning of these base states becomes clear. Pattern B is in the representation of all of the numbers except 1. Four Base Patterns Used in Dice Codes If you write down the truth table. The four switches on the front panel can now simulate turning on and off the base patterns. B. and D: A B C D Figure 2-3. On the diagram page. and 6. Figure 2-4. C. there are only four unique patterns from which the pattern for any face can be formed. Call these base patterns A. and 5). for the presence or absence of these base patterns as a function of die face. and D. The Die To build a virtual die. 5. C. together with four switches. 3.
and Q3. Place three LED indicators on the front panel. select the three outputs as connections in the icon editor and save this program as a subVI called Rotate. each wired to one LED indicator. Note that the While Loop control is left unwired. On the block diagram. Q2. Each time this VI is called. On the front panel. These will show the output state of the shift register elements called Q1. Figure 2-6.Lab 2 Encoders and Decoders Figure 2-5. the next value is returned. Modulo 6 Counter A modulo 6 counter is any counter with six unique states that repeat in sequence.) Open a new LabVIEW VI.vi and observe the operation of the virtual die. (Such a counter is often called a switched tail ring counter.vi. You can use a Wait function to slow down the action for demonstration. You can build a simple modulo 6 counter using a three-element shift register with the last element output inverted and feedback into the first element input. LabVIEW Block Diagram to Implement Virtual Die Display Load the VI Display. Rotate.vi Front Panel and Block Diagram © National Instruments Corporation 2-3 Fundamentals of Digital Electronics . use a shift register with three elements.
a three-input AND gate built in the last lab together with an inverter can be used. These two lines then decode two of the base patterns for "free. could signify odd states 1. for example Q3." The two remaining base patterns are decoded with a particular pattern of the three counter lines. One of these outputs. 5.Lab 2 Encoders and Decoders Below is the truth table for the modulo 6 counter. 6. 3. for example Q2′. To this end. hence the name modulo 6 counter. Run the program seven times to observe the action. Not 1 (Base Pattern B) is decoded with the combination Q1 & Q2 & Q3. However. each output has three (1) states and three (0) states. Table 2-2. Another output state. and 5. can then signify the family 4. Fundamentals of Digital Electronics 2-4 © National Instruments Corporation . Digital Die Encoding Scheme # 6 4 2 1 3 5 Q1 0 1 1 1 0 0 Q2 0 0 1 1 1 0 Q3 0 0 0 1 1 1 Q1′ 1 0 0 0 1 1 Q2′ 1 1 0 0 0 1 Q3′ 1 1 1 0 0 0 For example. and the final base state "6" is decoded with Q1′ & Q2′ & Q3′. Encoder There is no a priori reason to decide which output corresponds to which count. Truth Table for Modulo 6 Counter Cycle 1 2 3 4 5 6 7 Q1 0 1 1 1 0 0 0 Q2 0 0 1 1 1 0 0 Q3 0 0 0 1 1 1 0 same as cycle 1 The output repeats after six counts. a little foresight makes the choices easier: Table 2-3.
The encoder is wired by translating the words of the above paragraph into a circuit. A clock with a speed greater than 1 kHz ensures the randomness of the roll. In practice. Virtual Dice (modulo 6) Counter stop Figure 2-8.vi Front Panel and Block Diagram The encoder is built by placing three Boolean indicators on the front panel together with four LED indicators. Whatever state the counter has on its output will be the roll value. An encoder VI converts the three counter lines into the four control lines for the base patterns. Just as you would build electronic circuits by assembling gates. switches. latches. encoder and display—into a VI called Dice. It is now a simple case of assembling all the components—counter. and displays. Function Schematic for Digital Dice Encoder To roll the virtual die.Lab 2 Encoders and Decoders Figure 2-7. These in turn set the dots on the virtual die to the correct output code. These states are encoded on three output lines. © National Instruments Corporation 2-5 Fundamentals of Digital Electronics . a high-speed counter will cycle through the six states. Encode. the counter cycles until a stop command is issued to the counter. LabVIEW simulates this process by building complex functions from simpler ones.vi.
Note the Similarity with the Function Schematic Above Now.vi (LED displays for virtual die) Rotate.vi (converts counter codes to display codes) 3 AND.vi (modulo 6 counter) Encoder.Lab 2 Encoders and Decoders Figure 2-9.vi) Dice.vi Block Diagram. Dice.vi (subVI used in Encoder.vi (let the good times roll) Fundamentals of Digital Electronics 2-6 © National Instruments Corporation . flip the front panel switch and let the good times roll! Lab 2 Library VIs (Listed in the Order Presented) • • • • • Display.
but "10". when you add 1 + 1 in binary addition. it is helpful to review some details of binary addition. adding 0 to any value leaves that number unchanged: 0 + 0 = 0. one for each addend. and two output columns. "One and one are two. the result is not "2" (a symbol which does not exist in the binary number system). Single-Bit Addition Below is the truth table for single-bit addition. Just as in decimal addition. A1 and A2. There are two input columns. a "1" in the "twos place" and a zero in the "ones place. write down the zero. one for the ones-place sum and one for the carried bit: Table 3-1. you would recite. while 1 + 0 = 1." If you write this addition vertically. However.Lab 3 Binary Addition Before proceeding with this lab. carry the one": 1 +1 10 Figure 3-1. Truth Table for Addition A1 + A2 0 0 1 1 0 1 0 1 = Sum with Carry 0 1 1 0 0 0 0 1 © National Instruments Corporation 3-1 Fundamentals of Digital Electronics .
which adds the bit carried from the previous column. In addition to the two addends.Lab 3 Binary Addition Which of the fundamental gates can you use to implement the output columns? Note that A1 XOR A2 reproduces the Sum output. it cannot accept a carry from a lower-order adder. Three-Bit Binary Addition The truth table for a single-bit full adder therefore has three inputs. Half Adder Built from XOR and AND Gates This digital building block is called a "half adder. and A1 AND A2 the Carry output. there is also a "carry in" input. Truth Table for Addition with a Carry In Carry In 0 0 0 0 1 1 1 1 A1 0 0 1 1 0 0 1 1 A2 0 1 0 1 0 1 0 1 Sum 0 1 1 0 1 0 0 1 Carry Out 0 0 0 1 0 1 1 1 Fundamentals of Digital Electronics 3-2 © National Instruments Corporation ." The term "half adder" refers to the fact that while this configuration can generate a signal to indicate a carry to the next highest order bit. as in the middle column in the following example: 101 +101 1010 Figure 3-3. so a LabVIEW implementation of this 1-bit addition truth table is Figure 3-2. A "full adder" has three inputs. and thus eight possible states: Table 3-2.
a 4-bit adder could be constructed in LabVIEW as: Figure 3-6.Lab 3 Binary Addition Note that all three inputs are essentially equivalent. Full Adder Using Two Half Adder SubVIs Note the simplicity achieved in the wiring diagram by using the half adders. Adder Expansion You can construct a device that adds multibit binary numbers by combining 1-bit adders. The © National Instruments Corporation 3-3 Fundamentals of Digital Electronics . One way to build a 1-bit full adder is by combining two half adders: Figure 3-4. the full adder simply adds the three inputs. Each single-bit adder performs the addition in one "column" of a sum such as 1011 +0010 1101 Figure 3-5. LabVIEW Block Diagram for 4-Bit Binary Addition Note that this VI uses four 1-bit full adders. If you plan to add only 4-bit numbers with this circuit. the lowest-order adder could be a half adder. 4-Bit Binary Addition (11+2=13) For example.
each time adding a pair of bits.vi.Lab 3 Binary Addition use of all full adders allows the 4-bit adder to have a carry-in input. On the first iteration.vi) Note how the four independent bits are formed into 4-bit arrays before passing into the interior of the For Loop. the wiring above is somewhat complicated and would become even more complex if you extended the adder to more bits. Full Adder. It uses two subVIs.vi and observe the addition of two 4-bit numbers. on subsequent iterations. Run both versions of the VI and confirm that their behaviors are identical. starting at the least significant bit. as well as the two 4-bit addend inputs. By using a LabVIEW For Loop with a shift register. which iterates four times. As you can see. 4-Bit Adder Using Array Inputs and Outputs Fundamentals of Digital Electronics 3-4 © National Instruments Corporation . you can simplify the wiring significantly: Figure 3-7. shown in Figure 3-2. shown in Figure 3-4. the carry input to the 1-bit full adder is from the panel carry input. 4-Bit Binary Addition Using LabVIEW Arrays (Four-Bit Adder2. Load Four-bit Adder1. Figure 3-8. and Half Adder. it is the carry from the previous iteration.vi.
" and then the two "least significant nibbles" are sent to one 4-bit adder. Note that in Boolean arrays.Lab 3 Binary Addition There is also a third version of the above VI. 8-Bit Adder Using Two 4-Bit Adders Binary Coded Decimal (BCD) Not all digital arithmetic is performed by a direct conversion to the base-2 representation. the LSB is on the left and the MSB is on the right. and you can combine two of these to create an 8-bit adder. each decimal digit is separately encoded in four bits as follows: Table 3-3. BCD Representation for the Numbers 0 to 9 Decimal Digit 0 1 2 3 4 BCD Representation 0000 0001 0010 0011 0100 Decimal Digit 5 6 7 8 9 BCD Representation 0101 0110 0111 1000 1001 BCD can be considered to be a subset of full binary notation. This version has been configured as a subVI. which is identical to Figure 3-7 above except that the inputs and outputs are displayed as Boolean arrays. named simply Four-bit Adder3. Binary coded decimal. or BCD. in which only the states 0000 to 1001 (0 to 9) are used. while the two "most significant nibbles" go to a second 4-bit adder. 42 10 = 0100 0010 BCD © National Instruments Corporation 3-5 Fundamentals of Digital Electronics . In BCD. representation is also used. Figure 3-9. Note that each 8-bit (one-byte) addend is separated into two 4-bit "nibbles. For example.vi.
vi (adds two 4-bit numbers with carry in) Four-bit Adder2. because there are a number of 4-bit patterns that are not used to encode a decimal digit. The advantage of BCD is that it maps cleanly to decimal output displays.vi (single-bit addition with carry in) Four-bit Adder1. but the same two bytes will span only the range 0-9999 when using BCD. Two bytes (16 bits) is enough to encode unsigned decimal integers in the range 0-65535 if the binary representation is used.vi (uses two 4-bit adders) Fundamentals of Digital Electronics 3-6 © National Instruments Corporation . LabVIEW Challenge Create a BCD encoder that takes as its input a digit in the range 0-9 and outputs the 4-bit BCD representation.Lab 3 Binary Addition Note that this is distinct from the binary representation. Build a BCD decoder that reverses the behavior of the above encoder.vi (single-bit addition) Full Adder. Lab 3 Library VIs (Listed in the Order Presented) • • • • • • Half Adder. BCD is wasteful of bits.vi (simplified version) Four-bit Adder3. The waste becomes more pronounced for larger integers. which in this case would be 42 10 = 00101010 2 Clearly. Build a one-digit BCD adder.vi (uses Boolean arrays for inputs and outputs) Eight-bit Adder.
Lab 4 Memory: The D-Latch In the first three labs in this series. Clocked logic devices are devices whose output changes only when a clock signal is asserted. notes the state of its input and holds that state at its output. Most digital operations are sequential. © National Instruments Corporation 4-1 Fundamentals of Digital Electronics . The output state remains unchanged even if the input state changes. there is no dependence on past history or how you arrived at the current state. you will see how the addition of clocked logic devices brings memory into digital circuits. the input of the D-latch is designated by D and the latched output by Q. so-called edge-triggered devices or level triggered devices. in that event B must occur after event A. where the output follows the input whenever the clock is HI. events are not only sequential but also synchronous with some external clock. making it possible to construct many interesting digital circuits. in a digital computer. In the next few labs. One simple memory circuit is called the data latch. Furthermore. This is a device which. all your work has been with combinational circuits in which the input states completely determine the output states. when "told" to do so via the clock input. or D-latch. This means that "remembering" cannot be built into the circuits. Traditionally. until another update request is received. In the circuits thus far. The update command is provided by asserting the clock input in the form of a transition (from HI to LO) or (from LO to HI).
Lab 4 Memory: The D-Latch PreSet D D Clock Clr Q 0 1 Q Q Q 0 1 1 0 Set Clr 0 0 1 1 0 1 0 1 Q Q disallowed 1 0 0 1 clocked logic clocked Figure 4-1. using the Preset and Clear inputs when the clocked logic is not active. The up-arrow block is the D input. In normal operation. Fundamentals of Digital Electronics 4-2 © National Instruments Corporation . The complement is formed with an inverter tied to the Q output. Some D-latches also have Preset and Clear inputs that allow the output to be set HI or LO independent of the clock signal. LabVIEW Simulation of a D-Latch In LabVIEW. The clock input is analogous with the loop index [i]. shown above. you can simulate the D-latch with a shift register added to a While Loop. the outputs Q and Q can be initialized to a known state. and the down-arrow block is the output Q. However.vi. You can use a Boolean constant outside the loop to preset or clear the output. Figure 4-2. these two inputs are pulled high so as not to interfere with the clocked logic. a shift register is a cascade of 1-bit memories in which each bit is updated on a clock transition by copying the state of its neighbor. D Latch. D-Latch Symbol and Truth Tables Data present on the input D is passed to the outputs Q and Q when the clock is asserted. The truth table for an edge-triggered D-latch is shown to the right of the schematic symbol. Shift Registers In digital electronics. uses an unwired conditional terminal to ensure that the D-latch executes only once when it is called.
Block Diagram for an 8-Bit Shift Register It is a simple matter to add additional elements to simulate larger width shift registers.Lab 4 Memory: The D-Latch Q1 Q2 Q3 Q4 HI or LO D Q D Q D Q D Q Q Clock Q Q Q Figure 4-3. here is the 4-bit register. 4-Bit Shift Register The bits at the ends have only one neighbor. © National Instruments Corporation 4-3 Fundamentals of Digital Electronics . simulates a "bucket brigade" where a single bit is introduced on the input D and propagates down the line. Figure 4-4. The following VI.vi executes the above sequence.vi. For example. and the output Q4 spills off the other end of the shift register. where it spills out and is lost after passing Q8. Bucket. Shift. additional elements are added to the D-latch shift register. Here is an example of a 4-bit shift register whose initial output state is [0000] and input is [1]: Clock Cycle n n+1 n+2 n+3 n+4 Q1 0 1 1 1 1 Q2 0 0 1 1 1 Q3 0 0 0 1 1 Q4 0 0 0 0 1 To "cascade" D-latches as above in LabVIEW. The input bit D is "fed" from an external source (HI or LO).
A stepping motor with a 400-step resolution would then rotate 0. the parallel output eventually will repeat and the shift register now becomes a counter.Lab 4 Memory: The D-Latch Figure 4-5. Front Panel of an 8-Bit Shift Register Simulation LabVIEW Challenge Design a VI in which after the "bucket" passes the last bit. Modify Rotate. It takes four clock cycles.9 degrees each time the counter is called. In this case. 4-Bit Ring Counter Using Integrated Circuit Chips In the above case.vi. Observe how the outputs cycle from [0110] to [0011] to [1001] to [1100] and back to [0110]. Q4.vi. D. a new bucket is added at the input D. Ring Counters If the output of a shift register is "fed" back into the input. each change in output pattern results in the stepping motor advancing one step. Load and run Rotate. A simple 4-bit ring counter takes the last output.vi to make this change and save it as Switch Tail Ring Counter. and the process continues forever. Q1 Q2 Q3 Q4 D Q D Q D Q D Q Q Clock Q Q Q Figure 4-6. the outputs have been preset to [0110]. A slight variation of the ring counter is the switched tail ring counter. In a special case where these four outputs are passed to the current drivers of a stepping motor. hence this counter is a modulo 4 ring counter. and loops it back directly to the input of the shift register. after n clock cycles. The name ring counter comes from looping the last output bit back into the input. the complement output Q of the last stage is fed back into the input. Fundamentals of Digital Electronics 4-4 © National Instruments Corporation .
vi.vi (4-bit ring counter) Billboard. shown below.vi (8-bit shift register simulation) Rotate. Lab 4 Library VIs (Listed in the Order Presented) • • • • • D Latch.vi (4-bit shift register) Bucket.vi (16-bit ring counter used as a light chaser) © National Instruments Corporation 4-5 Fundamentals of Digital Electronics . Load and observe Billboard. and the 16 Boolean constants on the block diagram set the chase pattern.Lab 4 Memory: The D-Latch What is the modulus of the switch tail ring counter? Ring counters are often used in situations where events must be repeated at a uniform rate. which simulates a light chaser.vi (LabVIEW simulation of a data latch) Shift. You can use the slide control to set the speed of the changing lights.
Lab 4 Memory: The D-Latch Notes Fundamentals of Digital Electronics 4-6 © National Instruments Corporation .
In this lab.Lab 5 Pseudo-Random Number Generators In the last lab. and secure communications. A 6-Bit Pseudo-Random Number Generator In the following circuit. N = 8 and (2N-1) = 255. cryptography. bit error testing. have some interesting features. These circuits. The sequences formed appear to be random over the short range. Pseudo-random sequence and number generators have wide applications in computer security. audio systems testing. Furthermore. the outputs of the fifth and sixth D-latches have been exclusive NORed together to become the input to the shift register. the modulus of the counter is 2N-1). simple ring counters were introduced as a means of building modulo-n counters. 6-Bit PRNG Built from Six D-Latches and an XOR Gate © National Instruments Corporation 5-1 Fundamentals of Digital Electronics . but in fact the sequence repeats after (2N-1) cycles. the output is of maximal length (that is. For an 8-bit counter. each pattern occurs only once during each sequence of (2N-1) numbers. all outputs are zero. often called pseudo-random number generators (PRNG). D 1 C Q D 2 C Q D 3 C Q D 4 C Q D 5 C Q D 6 C Q Clock Figure 5-1. It is assumed that initially. feedback from a combination of advanced stages is combined and routed back into the input gate. If the correct combination is chosen.
and Q8 NXORed together to form the maximal length (2N-1) count sequence of 255. the output of the NXOR (see Lab 1) is 1. observe that cycles 0 and 63 are the same (that is. Q5. LabVIEW VI to Simulate a 6-Bit PRNG A six-element shift register is placed on a While Loop. When running this VI. An 8-Bit Pseudo-Random Sequencer An 8-bit PRNG uses the outputs Q4.vi. the sequence returns to the initial state (000000). This HI value is loaded into the shift register at the input D1. On command from the clock... all bits are zero). It is easy to work through a few cycles to see the outputs Q1. The loop index keeps track of the cycle count. Fundamentals of Digital Electronics 5-2 © National Instruments Corporation .Lab 5 Pseudo-Random Number Generators When Q5 and Q6 are 0. 6PRNG. all bits shift to the right. An exclusive OR gate and inverter are used for the NXOR gate whose inputs have been wired to Q5 and Q6. and a delay of 500 ms allows the reader to observe the PRNG patterns. Figure 5-2. It is easy to simulate this circuit with a LabVIEW VI. The initial value of (000000) goes to (100000). Q6.Q6 follow the sequence: (000000) (100000) (110000) (111000) ---------After 63 cycles.
In addition. Front Panel of the 8-Bit PRBS © National Instruments Corporation 5-3 Fundamentals of Digital Electronics . Many digital circuits need to be tested with all combinations of ones and zeros.vi.Lab 5 Pseudo-Random Number Generators Figure 5-3. a pseudo-random sequence of ones and zeros is produced at Serial Out. the parallel output can be observed on eight LED indicators. PRBS. LabVIEW Simulation of an 8-Bit PRNG As in the previous example. you can view the Boolean sequence [Serial Out] on an LED indicator. On the front panel of the above VI. the circuit is called a pseudo-random bit sequencer. Figure 5-4. In this configuration. A "random" Boolean sequence of ones and zeros at [Serial Out] provides this feature. PRBS0.
or a bit level may be outside specifications. the first 50 bits from PRBS. Any errors in transmission or lockup can be flagged. By resetting the scale of the second chart from 255 to 305. Here.vi. and passed to one side of a digital comparator. the PRBS driving sequence is passed to the other input of the comparator. Sometimes a laser may lock up from a particular sequence of ones and zeros.vi are displayed as a logic trace. The Boolean bits are converted into a numeric value of either 1 or 0 and then plotted on a LabVIEW chart. Comparison of the First 50 Binary Bits from a PRBS with Bits 255-305 Fundamentals of Digital Electronics 5-4 © National Instruments Corporation . two charts display the sequence. converted into a digital signal. Figure 5-6. At the same time. Figure 5-5. The laser output is detected by a photodiode. Serial Output from the Pseudo-Random Bit Sequencer Communication lasers are tested using PRBS waveforms. It is now easy to verify that the bit sequence repeats exactly after 255 cycles. In PRBS2. you can observe the repetitive nature of the PRBS.Lab 5 Pseudo-Random Number Generators A better way to view the bit sequence is as a bit trace.
Figure 5-8. All the numbers from 0 to 254 will be found in the PRNG sequence. In a binary conversion.vi allows you to observe the PRNG sequence of numbers. 8.. In the following VI. the parallel bits (Q1. 4. each number will appear only once in the sequence. Does the sequence appear random? The following block diagram is the LabVIEW simulation of an 8-bit PRNG. 16. Numeric Output from an 8-Bit PRNG Running PRNG.. and 128). Figure 5-7.Q8) are weighted as (1. 64.Lab 5 Pseudo-Random Number Generators 8-Bit Pseudo-Random Number Generator The addition of an analog-to-digital converter allows the parallel outputs of the pseudo-random number sequence to be converted into a numeric number. 2. and on closer inspection. LabVIEW Program for the 8-Bit PRNG with Chart Output © National Instruments Corporation 5-5 Fundamentals of Digital Electronics . 32. Note how the DAC displays the numerical values of the Boolean parallel outputs. the numeric values are displayed on a three-digit display and chart on the front panel.
but not long-term memory. Over the short range (10-30) numbers. When completed. but the sequence repeats itself in the usual way. a new Fundamentals of Digital Electronics 5-6 © National Instruments Corporation ." For each character in a message. or the character "z" in ASCII. The value of PRNG in audio testing is that the noise repeats after 2N-1 cycles. The addition of a parity bit to 7-bit ASCII codes yield an 8-bit digital number. and the PRNG converts this input character into an encrypted character by clocking the PRNG ahead N cycles. Suppose the initial value was (01111010). N. Its output is compared with the expected levels from the PRNG sequence.Lab 5 Pseudo-Random Number Generators The chart format conveniently displays the analog sequence. Figure 5-9. Boolean Array Representation of the 8-Bit Binary Pattern of the First Eight Numbers of an 8-Bit PRNG with the Patterns for Loops 262 to 268 Suppose a PIN or password is used to form a unique numeric code number. Encryption of Digital Data Most data communication takes the form of ASCII characters. Banking machines. Amplifiers like digital gates may have short-term memory. In the above example. it appears as white noise. or $7A in HEX. The PRNG sequence is just offset by this value. the character "z" would be encrypted as "X. the sequences are identical. In fact. the parallel outputs contain the encrypted character. Any deviation (errors) can reveal problems with the circuit under test. the sequence can begin at any initial value except the disallowed state (11111111). The PRNG is initialized by an ASCII character. if the PIN number was 257. or 122 in numeric. and computer passwords all use ASCII data and some form of encryption to preserve security. All cases thus far have used the LabVIEW default initialization of the shift register to start the PRNG sequence. Note that after 255 cycles plus this index (7 + 255 = 262). hence predictable. the output appears random and in fact is random from a mathematical perspective. electronic door locks. The PRNG analog output is applied to the analog circuit under test. Below is a Boolean array representation of 8-bit PRNG values starting at some index (7) and the next six values. As an analog output. The 8-bit PRNG is a useful circuit for encryption of ASCII data. repeating after 255 cycles.
Lab 5 Pseudo-Random Number Generators character is formed.vi (8-bit DAC subVI) © National Instruments Corporation 5-7 Fundamentals of Digital Electronics . and with the PIN. Lab 5 Library VIs (Listed in the Order Presented) • • • • • • 6PRNG.vi (8-bit PRNG with chart output) PRNG7.vi (8-bit PRBS with serial output on chart) PRNG.vi (6-bit PRNG) PRBS0.vi (8-bit PRNG with array outputs) DAC8. the original message can be deciphered. The receiver knows the encryption algorithm.vi (8-bit pseudo-random bit sequencer) PRBS.
Lab 5 Pseudo-Random Number Generators Notes Fundamentals of Digital Electronics 5-8 © National Instruments Corporation .
Lab 6 JK Master-Slave Flip-Flop One of the most important clocked logic devices is the master-slave JK flip-flop.K) inputs to (0. information can be placed onto the output bit and held until requested at a future time.1). This complement function is often referred to as bit toggling. When the J and K inputs are low. respectively. JK Flip-Flop Logic Symbol and Truth Tables The first entry of the clocked truth table is the memory state. and the resulting flip-flop (J and K inputs pulled HI) is called a T flip-flop. The output Q can be clocked low or high by setting the (J. Thus. which has memory only until another clock pulse comes along. What is new with the JK flip-flop is the fourth combination (1. Load Binary1. Set J clk K Clr Q Q clock J 0 0 1 1 K 0 1 0 1 Q Q no change 0 1 1 0 Set Clr 0 0 1 1 0 1 0 1 Q Q disallowed 1 0 0 1 toggle clocked clocked logic direct logic Figure 6-1.vi and observe the operation of the T-flip-flop on clocking. © National Instruments Corporation 6-1 Fundamentals of Digital Electronics . the JK flip-flop has true memory. which produces a toggle state.0). On clocking. placing an inverter between J and K inputs results in a D-latch circuit. Unlike the D-latch. The schematic diagram for the JK flip-flop and its truth table is shown below. Note that the JK flip-flop can also be Set or Reset with direct logic inputs. the state of the outputs Q and Q are unchanged on clocking. In fact. while the next two combinations are the latched states. it takes two clock cycles to return the output state to its initial state. the output changes from [1-->0] if 1 or [0-->1] if 0.1) or (1. Because only one toggle occurs per output cycle.
This is a modulo 4 binary counter. 0. the output frequency of the pair of flip-flops is (/2 and /2) or divide by 4. 0. Figure 6-3. In LabVIEW (see the block diagram and open the T flip-flop subVI).1. note on the block diagram how the output of the first flip-flop is ANDed with the clock to become the input of the next flip-flop.2. the T flip-flop is simulated with a Case structure placed inside a While Loop. Because two clock pulses are required for the output to cycle.Lab 6 JK Master-Slave Flip-Flop Figure 6-2. simulates the digital clock. The upper shift register. In the LabVIEW simulation.1.3.vi. the decimal equivalent values during clocking form the sequence 0. the T flip-flop divides the clock frequency by two and is often called a "divide-by-two" binary counter. If the output of one T flip-flop is used as the clock input for a second T flip-flop. Fundamentals of Digital Electronics 6-2 © National Instruments Corporation . with the inverter. the clock changes state from HI-LO or LO-HI.2.3. LabVIEW Simulation of a Divide-by-Four Binary Counter If the output of the first flip-flop is weighted as 1 and the second flip-flop as 2. Load and run Binary2.1.3. How many times do you need to press the Run button to cycle the output bit from LO-HI-LO? It may be easier to make the correct observation by pressing the Run Continuously button.2. etc. LabVIEW Simulation of a Divide-by-Two Counter Using a T Flip-Flop SubVI Each time the Run button is pressed.
K) inputs to a logic 1 (HI) and connecting the output of each flip-flop to the clock of the next flip-flop. In addition. which simulates the above binary counter. Four JKs in sequence divide by 24 or 16. The four binary states (Q3. Q0 Hi Hi Q1 Hi Q2 Hi Q3 J clock C K Q J C Q J C Q J C Q Q K Q K Q K Q Hi Hi Hi Hi Figure 6-4. and the result ripples down the chain. 4-Bit Binary Counter Built with JK Flip-Flops In this configuration.vi. The clock signal enters the chain at the clock of the first flip-flop. the clock signal is divided by 2 each time it passes through a JK flip-flop. Q0) are displayed as LED indicators. observe the operation of the divide-by-16 binary counter. © National Instruments Corporation 6-3 Fundamentals of Digital Electronics .Lab 6 JK Master-Slave Flip-Flop Binary Counters Binary counters are formed from J-K flip-flops by tying all the (J. and the decimal equivalent value as a numeric on the front panel. Q1. Load the 4-bit binary VI called Binary4. Q2. By pressing the Run button. the timing diagram is shown for the four outputs Q0-Q3 on four separate charts.
4-Bit Binary Count Sequence and Decimal Equivalent Values Clock Cycle 0 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 Q3 0 Q2 0 Q1 0 Q0 0 DE # 0 1 1 1 1 15 Fundamentals of Digital Electronics 6-4 © National Instruments Corporation .Lab 6 JK Master-Slave Flip-Flop Figure 6-5. Table 6-1. LabVIEW Simulation of a 4-Bit Binary Counter Observe the sequence and fill in the truth table below.
. For example.. all the binary numbers 0-15 can be represented on the four outputs. f/8. Binary counters need to be reset (all bits 0) or set (all bits 1) for various operations. and Q3 are weighted as 20. The output frequencies are f/2.9 and A.Lab 6 JK Master-Slave Flip-Flop The complete table displays all binary combinations for a 4-bit binary counter. In hexadecimal counting.vi demonstrates visually the binary counting sequence as a byte on eight LED indicators or as an 8-bit timing diagram. and each nibble is coded as one hexadecimal character. Q2. Summary Binary counters are a fundamental component in digital electronic circuits. the 16 states (0-15) are labeled as 0. f/16. and modern microprocessors use 16. respectively. Load and run this VI continuously. and f/256 for the output stages Q0. Run this VI continuously to observe binary numbers from 0-255. which counts from 00 to 99.vi provides a clear function for the 8-bit binary counter. LabVIEW Challenge Design a two-digit binary counter. These operations are exclusive. the binary counter is cleared. Look at the LabVIEW block diagram to see how the decimal equivalent value is calculated. the 16-bit binary number 1101 0111 0011 1100 is coded as $D73C hexadecimal. 21. f/64. A 0 on either the Set or Clear input forces the output to a 1 or 0. The VI Binary8. This notation is more compact and easier to remember than long combinations of binary bits.F. The truth table for the JK flip-flop shown above has direct inputs that provide this function. This operation is useful in applications for odd length counters and in designing analog-to-digital converters. hence the (00) state is disallowed.. They are used in all forms of modulo-n counters. By pressing the Reset button. f/4. The VI Bin8_Reset.or 32-bit data paths. f is the clock frequency. Larger bit lengths are subdivided into groups of 4 bits called a nibble. Q1. Here. If the outputs Q0.. and 23.. in the generation of harmonic clock subfrequencies. 8-Bit Binary Counter A logical extension of the 4-bit binary counter is to higher data widths. The timing diagram clearly shows how each stage divides the previous output by 2. 22. The clocked logic can occur whenever the reset and set inputs are pulled high. f/32. f/128. Embedded controllers use an internal 8-bit data bus. © National Instruments Corporation 6-5 Fundamentals of Digital Electronics .. and in many higher order functions such as digital-to-analog and analog-to-digital devices.Q7.
vi (Divide by 16 binary counter with logic traces) Binary8.Lab 6 JK Master-Slave Flip-Flop Lab 6 Library VIs (Listed in the Order Presented) • • • • • • Binary1.vi (Divide by 4 binary counter) Binary4.vi (Divide by 2 binary counter) Binary2.vi (8-bit binary counter with external reset button) FlipFlop.vi (T flip-flop subVI used in above programs) Fundamentals of Digital Electronics 6-6 © National Instruments Corporation .vi (Divide by 256 binary counter with logic traces) Bin8_Reset.
known as the D/A converter (read as D-to-A converter) or the DAC. several variations. What is a DAC? A DAC is an electronic component that converts digital logic levels into an analog voltage. bi is the bit value (1 or 0). DACs are the core of many circuits and instruments. is a major interface circuit that forms the bridge between the analog and digital worlds. including digital voltmeters. This chapter examines the digital-to-analog converter.Lab 7 Digital-to-Analog Converter The digital-to-analog converter. oscilloscope displays. and many computer-controlled devices. plotters. In the case of a binary weighting scheme. The output of a DAC is just the sum of all the input bits weighted in a particular manner: DAC = ∑w b i=0 i i where wi is a weighting factor. and how it is used for waveform generation. and i is the index of the bit number. wi = 2i. the complete expression for an 8-bit DAC is written as DAC = 128 b7 + 64 b6 + 32 b5 + 16 b4 + 8 b3 + 4 b2 + 2 b1+ 1 b0 © National Instruments Corporation 7-1 Fundamentals of Digital Electronics .
The diagram panel displays the LabVIEW algorithm shown below for the 8-bit converter. LabVIEW VI for 8-Bit DAC.vi demonstrates the conversion process. Eight LED indicators display the binary value of the input byte when the simulation is run. DAC. On the front panel. which Fundamentals of Digital Electronics 7-2 © National Instruments Corporation .Lab 7 Digital-to-Analog Converter Figure 7-1. The analog output is displayed as a numeric indicator. eight Boolean switches set the input bits b0 through b7. LabVIEW Simulation of an 8-Bit DAC The above simulation. Figure 7-2. Note the Boolean-to-Real icon on the block diagram.vi The simulation uses two input multiply and add functions to generate the DAC sum.
Load and run DAC. Observe the operation of the carry bit.R2 which adds the contents of Register 1 with the contents of Register 2 and stores the sum into an accumulator.R2. Nine LED indicators show the value of the accumulator and any overflow in the carry bit. Try adding simple sequences such as (1+1) to more complicated patterns such as $EF +$3. Consider the add instruction ADD R1. This VI can add larger bit values such as 16-bit numbers. ALU Simulator The arithmetic and logic unit (ALU) is responsible for all arithmetic and logic operations occurring inside the central processing unit (CPU) of a computer chip. © National Instruments Corporation 7-3 Fundamentals of Digital Electronics . you will see how the binary addition modules of Lab 3 have been used with the DAC. On the block diagram. To see how a DAC might be used.Lab 7 Digital-to-Analog Converter simulates in a very real way the bridging of the binary (Boolean levels) into the analog (numeric) value. Eight Boolean switches and displays simulate the 8-bit registers R1 and R2.vi modules to complete the simulation. DAC. Three copies of DAC. so it can be used in other programs to convert any 8-bit digital signal into the decimal equivalent value. LabVIEW Simulation of an 8-Bit Binary Adder Load and run ADD R1.vi is also a subVI.vi to observe 8-bit binary addition in action.vi to observe the relationship between the binary codes and their numeric equivalent.vi convert the contents of the three registers into their numeric equivalent value. Figure 7-3. consider the simulation of an 8-bit add instruction inside a microcomputer chip.
28 ma = 1. The transfer function found in the DAC specifications is i = K {A1/2+A2/4+A3/8+A4/16+A5/32+A6/64+A7/128+A8/256} where the digital inputs Ai = 0 or 1. This is a convenient scaling constant.9 kW) 3 2 VEE (–15v) Figure 7-4.Lab 7 Digital-to-Analog Converter Simulating a Real DAC Chip The Motorola MC1408 is an 8-bit digital-to-analog converter that provides an output current. all bits high. Fundamentals of Digital Electronics 7-4 © National Instruments Corporation .0 kΩ. . For a feedback resistor of 2.55 V. i. configured as a current-to-voltage converter. Vref(+5v) R14 A1 . MSB 13 5 6 7 8 9 10 11 12 16 15 pF 14 VCC(+5v) 2. the maximum output is . and here A1 is the most significant bit. has a decimal equivalent value of 255. which equals 1. The maximum current produced when all input bits are high is 0.9 kW) +15v MC 1408 4 2 – 7 . MC741.iR. directly proportional to the digital input. and the proportionality constant K = Vref / R14.28 ma through the resister R14. A8 is the least significant bit.275 ma.0 kW (3. converts the DAC current into a voltage. 8-Bit DAC Circuit Built with Conventional Integrated Circuits An operational amplifier.2.9 kΩ. A8 R15 15 741 3 + 4 –15v 6 Vout LSB (3. The reference voltage taken here as +5 V supplies a reference current of 5 V/3. because the maximum digital input. Vout = .996 * 1. and the sensitivity is 10 mV/bit.
For this demonstration. which simulates a DAC circuit using the 1408 DAC chip. the larger the slope.vi.vi introduced in Lab 5 is connected to DAC. The slope of the ramp is set by the frequency of counts—the larger the frequency. the output can be scaled to any convenient full scale value (for example. the VI Binary8.vi. as it resembles a stairway. An oscillator module generates the clock signal. By adjusting the feedback resistor. 1 bit change) is 10 mV.000). Note the differences on this block diagram as compared to the DAC. If you have access to an MC1408 DAC and 741 OpAmp. Waveform Generators Any sequence of bits fed to the inputs of the DAC at a uniform rate can be used to produce an analog waveform.vi block diagram. 1. This digital ramp is sometimes called a staircase waveform. This will generate a 0-2. Observe that the DAC resolution (that is. the simulation can be compared with the real circuit shown in the schematic diagram. When the binary counter overflows from (11111111) to (00000000). Its output is then connected to a waveform chart. © National Instruments Corporation 7-5 Fundamentals of Digital Electronics . LabVIEW Simulation of the 8-Bit DAC Circuit Shown in Figure 7-4 Load and study the VI MC1408.Lab 7 Digital-to-Analog Converter Figure 7-5.55 V digital ramp waveform. the analog voltage falls sharply from 255 to 0. The simplest sequence is derived from the outputs of an 8-bit binary counter.
6-Bit.vi.Lab 7 Digital-to-Analog Converter Figure 7-6. the digital waveform more closely approximates an analog ramp.vi demonstrates a signed analog output. In the analog world. and an 8-bit DAC has 255 steps. Take a look at the output of DAC8/12. which demonstrates the added resolution in moving from an 8-bit to a 12-bit DAC. Special DACs In unsigned binary arithmetic. all the numbers are positive. as the number of bits increases from 16 to 20. In this case. In the limit. Output of a 4-Bit. such a waveform is called a sawtooth wave. Most engineering and scientific applications require at least 12-bit resolution. A 4-bit DAC has 15 steps.vi. called DAC Resolution. Signed arithmetic uses the most significant bit to indicate the sign of the number (0 is positive and 1 is negative). Fundamentals of Digital Electronics 7-6 © National Instruments Corporation . the height of the stair step shrinks in size. demonstrates dynamically how the resolution is increased with bit width. The VI named DAC+/-. The above simulation. the 256 binary values of an 8-bit DAC are divided into the positive numbers from 0 to 127 and negative numbers from -128 to -1. a 6-bit DAC has 63 steps. and 8-Bit DAC As the number of bits of the DAC increases.
vi and investigate the phase relationship of two harmonically related signals. there are four intersection points on a horizontal line and two on a vertical line. you can find the ratio of the two frequencies. Lissajous Figures If two signals are harmonically related. Figure 7-8. a plot of one on the x-axis against the other on the y-axis yields interesting patterns called Lissajous figures. Unsigned and Signed DAC Output Note that the range of Y is identical for both the signed and unsigned version. By counting the number of intersection points a horizontal line makes with the pattern and dividing by the number of intersection points a vertical line makes with the pattern. giving a ratio of 2:1. Load Lissajous1. the Lissajous pattern can also give the phase between the two signals. if the two signals are perfect harmonics.Lab 7 Digital-to-Analog Converter Figure 7-7. LabVIEW Simulation for a Lissajous Plot ω2=2*ω1 © National Instruments Corporation 7-7 Fundamentals of Digital Electronics . In addition. In the following example.
vi (subVI used in ADD R1.vi (subVI used in ADD R1.vi) FlipFlop.vi) Full Adder.R2.R2.vi (simulation of a Lissajous plot) DAC8/12.vi (4-bit.vi (unsigned and signed DACs) Lissajous.vi (simulation of a Motorola 1408 DAC IC) DAC Resolution.vi) BIN_RST.vi (resolution of an 8-bit and a 12-bit DAC) DAC12.vi (8-bit binary adder) MC1408. 6-bit and 8-bit DAC simulation) DAC+/-.vi (subVI used in DAC8/12.R2.vi) Fundamentals of Digital Electronics 7-8 © National Instruments Corporation .Lab 7 Digital-to-Analog Converter Lab 7 Library VIs (Listed in the Order Presented) • • • • • • • • • • • • DAC.vi (8-bit DAC simulation) ADD R1.R2.vi (8-bit binary counter with reset) Half Adder.vi (subVI used in ADD R1.
Part I The analog-to-digital converter. oscilloscopes. The fundamental conversion process is shown in the following diagram. Purpose of the Analog-to-Digital Converter The purpose of an ADC converter is to produce a digital binary number that is proportional to an analog input signal. of which the ramp. digital multimeters. is the second key component to bridging the analog and digital worlds. and many other instruments. and successive approximation converters are common. If the input signal is larger than the test signal. the counter is increased to bring the test signal closer to the input level.) The test voltage is then compared with the input signal. Symbolic Design for an 8-Bit Analog-to-Digital Converter A counter creates a test binary sequence. There are many different ADC designs. and its digital output is converted into an analog voltage using a digital-to-analog converter. (This is a good time to review its operation if you are not familiar with the DAC. The DAC is a basic element of many ADC circuits and was discussed in Lab 7. known as the A/D converter (read as A-to-D converter) or the ADC.Lab 8 Analog-to-Digital Converters. Input Voltage + C – Test Voltage DAC b7 Counter b0 Reset Figure 8-1. the counter is decreased to bring the test signal closer to the input level. If the input signal is smaller than the test signal. The ADC is the basis of digital voltmeters. multichannel analyzers. This lab looks at the ramp and tracking A/D converters. tracking. The © National Instruments Corporation 8-1 Fundamentals of Digital Electronics .
However. Part I process continues until the comparator changes sign.vi and follow the action on the front panel. LabVIEW VI to Simulate an 8-Bit Ramp ADC The last value on the binary bits (b7-b0) is the digitized value of the input voltage level. the comparator will change sign and stop. The comparator function is simulated with the LabVIEW Equal function.vi. Try other values of the input level and note that the conversion time depends on the input voltage level. a wait time of 60 ms is chosen so that the eye can follow the action. In the LabVIEW simulation. In this demonstration.Lab 8 Analog-to-Digital Converters. Increasing the number of bits of the counter and DAC increases the conversion resolution. together with the 8-bit DAC. Load and run the simulation VI Ramp. at which time the test level will be within one count of the input level. equal to—the input level.vi (introduced in the last lab). an 8-bit binary up counter. Fundamentals of Digital Electronics 8-2 © National Instruments Corporation . when the test level becomes greater than—or in this case. Binary Counter. generate the test waveform. The test level will rise from 0 to 255 and repeat if left in the free running mode. The Ramp ADC The ramp ADC uses a binary counter and digital-to-analog converter to generate a ramp test waveform. DAC. Figure 8-2.
the binary counter is allowed to free run. This intersection of the ramp waveform with the input level can be seen on a chart display. the binary counter resets. The conversion time is thus dependent on the input signal magnitude and the clock circuitry speed. If the changing state of the comparator resets the binary counter. The transition of the comparator indicates this event. In the display below. Load the VI Ramp2. the binary counter is replaced with the binary counter with reset.vi. Figure 8-4. but for 12-bit DACs. this property is a disadvantage.Lab 8 Analog-to-Digital Converters. is that the conversion time depends on the magnitude of the input signal. Small input levels are digitized faster than large input levels. Note that as soon as the test level reaches the input level. featured in Lab 6. Part I Figure 8-3. Chart Display of the Ramp ADC in Operation An interesting feature. the comparator changes sign. In this case. The Comparator LED Indicator Changes State When the Test Waveform Numeric Value Exceeds the Voltage Input In the next simulation. the input level was changed three times. unique to the ramp ADC. For an 8-bit DAC. a true ramp ADC is simulated. © National Instruments Corporation 8-3 Fundamentals of Digital Electronics . Ramp4. Whenever the test signal is greater than the input level. variable conversion times may not be a problem when the clock is running at megahertz frequencies.vi and observe the action. The binary value of the counter at the intersection point is the digitized signal. and the ramp cycle starts all over again. LabVIEW Front Panel of 8-Bit ADC Converter.
Tracking ADC The first task for the tracking ADC is to use some technique such as a ramp waveform to catch up to the input level. Figure 8-5. Once the input level is reached. a positive ramp ADC technique is used to initially catch up to the input level of 150. LabVIEW Challenge Design a ramp ADC that uses a down counter to generate the test waveform. Part I The ramp ADC works equally well with a down counter that runs from 255-0.Lab 8 Analog-to-Digital Converters. decrease the count by one else if test level is less than the signal level. and it has the fastest conversion time. The change of state of the comparator again signals the binary count that generates a test level equal to the input level. Tracking ADC Ramps Up to the Input Level Before Tracking Begins The tracking algorithm is simply. shown by the intersection of the ramp waveform with the input level. At that point. In the following example. such a conversion technique is called a tracking ADC. the tracking algorithm takes over.2. increase the count by one and repeat forever. Fundamentals of Digital Electronics 8-4 © National Instruments Corporation . if test level is greater than the signal level. Could you use an up/down counter to track the input level? Yes. the tracking algorithm takes over.
Part I By expanding the vertical scale.Lab 8 Analog-to-Digital Converters. you can see the tracking algorithm in action. the digitized signal is lost until the test level catches up again. © National Instruments Corporation 8-5 Fundamentals of Digital Electronics . Tracking ADC Output when Input is Constant However. In practice. it is the slewing speed of the DAC that limits the maximum input frequency that the tracking ADC can follow. But if the signal changes too quickly. if the input level changes. A Sudden Change in the Input Level Causes the Test Level to Ramp Up to the New Level Because the tracking ADC uses an up/down counter. the algorithm has the same problem when the input signal suddenly falls below the test level. the tracking can keep pace. The tracking ADC reverts to a down ramp (Figure 8-8) until the test level reaches the input signal level. Figure 8-7. Figure 8-6. the ADC must revert to a ramp waveform to catch up to the input level. Provided the clock is fast enough.
10 second so that the user can observe the action on the front panel. A LabVIEW Select function and the shift register on the While Loop implements the algorithm. You can also use the Operating tool to redefine the vertical axis scale to zoom in on the action as the simulation is in progress. conversion slowed for easy viewing) Ramp4.vi Binary Counter. Figure 8-9. LabVIEW VI for the Tracking ADC The Wait function is set to 0.vi (8-bit ramp ADC. reduce the input constant for the Wait function in Figure 8-9 to 1 ms. Lab 8 Library VIs (Listed in the Order Presented) • • • • • • • • Ramp. A Negative Change in the Input Level Causes the Test Level to Ramp Down to the New Level The VI called Tracking ADC. The algorithm shown on the block diagram is quite simple. To observe the tracker catching up to a varying input.vi (subVI 8-bit DAC) FlipFlop.vi (8-bit ramp ADC with chart output) Tracking ADC1.vi is used to demonstrate this technique and to generate all the above charts.vi (ramp ADC with no feedback from comparator) Ramp2.vi (subVI 8-bit binary counter) BIN_RST.Lab 8 Analog-to-Digital Converters.vi (subVI 8-bit binary counter with external reset) DAC.vi (subVI) Fundamentals of Digital Electronics 8-6 © National Instruments Corporation . Part I Figure 8-8.
Reset the SAR register and set the DAC to zero. having the value of 128. On the next cycle. 128 + 64 = 192). Because 128 is less than 153. reading right to left. The SAR algorithm is as follows: 1. and the best estimate remains (1000 0000). the test value is greater than the input © National Instruments Corporation 9-1 Fundamentals of Digital Electronics . is to be tested first. In the following cycle. 4. Part II In the last lab. 2. the digital output of the SAR will contain the digitized value of the input signal. This algorithm can best be seen with the aid of a graph of the input signal level and the DAC waveform produced by the SAR. leave the bit on. Set MSB of SAR: if VDAC is greater than Vin. 3. Again. Repeat step 2 for the next MSB. These ADCs are substantially faster than the ramp ADCs and have a constant and known conversion time. SARs make use of the binary weighting scheme by outputting each bit in succession from the most significant bit (MSB) to the least significant bit (LSB). else if VDAC is less than Vin. The best estimate after the first cycle is (1000 0000). then turn that bit off. In binary. After n cycles. this bit is not kept. the next MSB. is added to the best estimate (that is. The number 153 is 128 + 16 + 8 + 1. having value 64. the MSB is to be kept.Lab 9 Analog-to-Digital Converters. Because 192 is greater than 153. binary counters in the form of up and up/down counters were used to create test waveforms for ramp and tracking ADCs. Another popular ADC is based on a test waveform created from a successive approximation register (SAR). the number is 15310 = (10011001)2 The SAR algorithm states that the MSB. Suppose a value of 153 is input into the ADC circuit. the next bit value of 32 yields a test value of 128 + 32 = 160. until all n bits of the SAR have been set and tested.
Digitized Value of an SAR ADC Displayed as a Boolean Array Fundamentals of Digital Electronics 9-2 © National Instruments Corporation . Successive Approximation Waveform Used to Digitize Input Voltage Load the VI named SAR. and the dashed line is the input level of 153. Figure 9-2. so this bit is not kept. Part II level.Lab 9 Analog-to-Digital Converters. Most ADCs based on SARs have conversion times of less than 100 ms. digitizing the input level in all cases in the same 8 cycles. Figure 9-1. After 4 cycles. In the following cycle. the timing diagram shows precisely this process. The DAC output MSB settling time sets the fundamental speed limitation. and the SAR test waveform will dutifully follow. This value is less than 153. and the best estimate remains at (1000 0000). The remaining cycles can be seen on the LabVIEW simulation for a successive approximation analog-to-digital converter. The solid line is the test value for each cycle.vi and run the VI in the continuous mode. so this bit is kept. the best estimate is (1001 0000). the next test value of 16 yields 128 + 16 = 144. In the panel below. You can use the Operating tool to change the input level. Continuing for the next four cycles yields the final binary value displayed on eight LED indicators.
Initially. the SAR0. 8. The compare function decides whether the current bit should be included in the new best value. The input level is set to 153. As a result. After the 8 cycles of the SAR. LabVIEW Simulation of the SAR Algorithm Using Shift Registers To generate a binary representation of the best estimate. with each bit value added to the previous best estimate as discussed above. and 1) as the loop counter cycles from 0 to 7. The test bit is formed by taking the number 256 and successively dividing it by two in a shift register eight times. 64. as is a real SAR chip. Part II A second VI. SAR Simulation The LabVIEW simulation is somewhat complex. the array contains the digitized value. 4.vi. SAR0. © National Instruments Corporation 9-3 Fundamentals of Digital Electronics . a Boolean accumulator in the form of a Boolean shift register is used. the SAR algorithm. either a high or low. Figure 9-3. 2. The sequence at the Bit Value will read (128. slows the action so you can watch each cycle. The digitized value is the best estimate of the input level after 8 cycles. The Test Bit. the eight-element array is set to Boolean False states to ensure that all LED indicators in the Boolean array are off. The ninth loop is needed to load the initial values into the shift registers.16. The Boolean array of indicators shows the binary value of the best estimate as it is developed. 32. The test value is formed by adding the new bit value to the previous best estimate. and after the 8 cycles. is passed in the array after each cycle using the LabVIEW Replace Array Element function. The test level is the DAC output.Lab 9 Analog-to-Digital Converters. and then the binary representation using a Boolean array.vi block diagram will be discussed in two parts—first. The Boolean True or False is loaded into the Boolean array at the index specified by the loop counter. the best value is the digitized level.
In SAR_Hex.vi. Summary In the last two labs. Try running this VI. a two-character string representing a hexadecimal number from $00 to $FF is converted into a numeric from 0 to 255 and digitized using the SAR algorithm with arrays. as long as no rapid changes in the input signal level occur. The overall best choice is the successive approximation ADC. The LabVIEW string function Format and Strip formats any string input into a number according to the selected conversion code. The ramp ADC is conceptually the simplest. but suffers from a variable conversion time proportional to the input signal magnitude. with a constant and known conversion time. Part II Figure 9-4. Lab 9 Library VIs (Listed in the Order Presented) • • • SAR.Lab 9 Analog-to-Digital Converters. three types of analog-to-digital converters were introduced and demonstrated. the binary value is complete.vi (SAR ADC with a hexadecimal input) Fundamentals of Digital Electronics 9-4 © National Instruments Corporation .vi (SAR ADC slow version for observing the conversion process) SAR_Hex.vi (successive approximation register ADC) SAR0. LabVIEW Simulation of SAR Using Arrays As the best estimate is built. The tracking ADC is the fastest converter. After the 8 cycles. the digitized binary value shows up on the front panel. and its decimal equivalent is identical to the digitized value shown in the numeric display.
For most simple instruments. b. c. a segment can be formed. Seven-Segment Display Uses Seven LED Bars The individual segments are coded a. d. d. and g and are ordered clockwise. E. When an LED is forward biased. By shaping the LED as a horizontal or vertical bar. You have seen how parallel combinations of ones and zeros can represent binary. Seven-Segment Display The LED seven-segment display uses seven individual light emitting diodes. with the last segment (g) as the central bar. b. An eighth diode in the shape of a dot is available on some seven-segment displays to indicate a decimal point. © National Instruments Corporation 10-1 Fundamentals of Digital Electronics . e. or digital numbers. light is emitted. f. c. configured as the number 8 in the pattern shown below: a f b g e d c Figure 10-1.Lab 10 Seven-Segment Digital Displays Digital displays link the digital world of ones and zeros with numerics of the human world. Each segment is controlled by a single bit. and F. digital displays use the numbers 0-9 and are represented by seven segmented displays. hexadecimal. such as A. and combinations of segments turned ON or OFF can display all the numbers 0-9 and a few characters. Many output devices such as computer parallel ports are 8 bits wide.
try outputting the message "help call 911" one character at a time. bit 7. LabVIEW Simulation of a Seven-Segment Display The input bits 0-7 are represented by eight Boolean switches. How many characters in the alphabet can you display? Figure 10-2. Try different combinations of the switches.vi simulates this task. The first step in a LabVIEW simulation is to convert the 4-bit binary nibble into a number from 0 to 15.vi. The corresponding segments in the seven-segment display are traditionally labeled a to g and dp (decimal place). The most significant port bit. Figure 10-3. which is a LabVIEW simulation for a seven-segment display. The VI named Bin->Digit. The least significant bit 0 is wired to segment a. By operating the switches. Most seven-segment displays are driven with an encoder that converts a binary encoded nibble into a numeric number. Front Panel of the 4-Bit Binary-to-Digit Conversion Program Fundamentals of Digital Electronics 10-2 © National Instruments Corporation . is often wired to an eighth LED and used as a decimal point. After experimenting with the display. the next bit 1 is wired to segment b. which in turn selects the appropriate seven-segment code.Lab 10 Seven-Segment Digital Displays Run the VI 7 Segment. etc. you can display all the numbers and a few characters.
In Encoder Hex. LabVIEW VI for a 4-Bit Digital-to Analog Converter The next step is to convert the digit(s) 0 to 15 into the appropriate seven-segment display. The correct address must be entered © National Instruments Corporation 10-3 Fundamentals of Digital Electronics .Lab 10 Seven-Segment Digital Displays On the block diagram. all the way to F. number 1 outputs the code for 1.vi. LabVIEW VI for Numeric-to-Seven-Segment Display The hexadecimal number inside the square box is the hexadecimal representation for the 8-bit pattern necessary to represent the number. etc. The number 0 outputs the seven-segment code for zero. multiple case statements are used to provide the encoder function. Figure 10-4. The Boolean constants inside each Case statement are initialized to generate the correct seven-segment code. a 4-bit digital-to-analog converter completes the operation. The Case terminal ? is wired to a numeric control formatted to select a single integer character. a single hexadecimal character [A to F] is used. Figure 10-5. For the numbers 10 to 15. Each port has a unique address that must be selected before data can be written to or read from the real world.. #n.
vi and Encoder. can be combined to form a binary-to-seven-segment encoder and display. Hexadecimal-to-Seven-Segment Display Encoder and Indicator Select the port address 1 and run Encoder. 0 to 15. In this simulation. Figure 10-6. click on the slider and drag it along the range of numbers. these outputs are passed to a seven-segment display. Bin->Digit. Load and run the VI Display7.vi. First.Lab 10 Seven-Segment Digital Displays on the front panel to access the port. With the Operating tool. the input would be a 4-bit binary number and the output would be the seven-segment code for the binary bit pattern. 4 binary 16 line encoder 16 7 segment encoder driver Figure 10-7. Finally. which emulates this operation. You can see all numbers encoded as a seven-segment hexadecimal character. Symbolic Diagram of a Binary-to-Seven-Segment Display Circuit In general. These two VIs. These outputs then select the appropriate seven-segment code. the 4-bit binary nibble is converted to one of 16 outputs.vi. Fundamentals of Digital Electronics 10-4 © National Instruments Corporation . the address operates the run command.vi.
vi (hexadecimal encoded binary-to-seven-segment display) © National Instruments Corporation 10-5 Fundamentals of Digital Electronics .vi (LabVIEW simulation of a seven-segment display) Bin->Digit. hexadecimal version) Display7.vi (seven-segment display.Lab 10 Seven-Segment Digital Displays Figure 10-8.vi (4-bit digital-to-analog converter) Encoder Hex. Use the 8-bit binary counter from Lab 6 modified to count in decimal. Binary-to-Seven-Segment Front Panel LabVIEW Challenge Design a two-digit counter that counts from 0 to 99. Lab 10 Library VIs (Listed in the Order Presented) • • • • 7Segment.
Lab 10 Seven-Segment Digital Displays Notes Fundamentals of Digital Electronics 10-6 © National Instruments Corporation .
At a minimum. time is represented as moving from left to right. the protocol demands that the least significant bit.33 ms. the output line is pulled high or low and then held in that state for the timing period. in reverse order. and a reference ground. or in LabVIEW as a Boolean True. the frequency of data transmission measured in bits per second. For example. This timing period is the reciprocal of the Baud rate. The standard bit serial format. Transmit Line Receive Line Ground Line Figure 11-1.Lab 11 Serial Communications Many instruments. RS-232. these transitions and levels form a serial waveform. Consider an 8-bit data byte $3A (or in binary. In RS-232 communication. only three communication lines are needed for communication between a computer and an external device: transmit. By convention. controllers. be transmitted first and the most significant bit. Serial Communication Lines In serial communications. This falling edge or negative transition is the signal for the receiver to get ready for incoming data. (0011 1010)). The ability to communicate to these devices over a serial interface opens a whole new world of measurement and control. all data bits are sent and held for a constant period of time. Together. receive. The transmitter signals the receiver that it is about to send data by pulling the transmit line low to the space state (0). while the low level is called the Space state. the output line is in a high state. last. defines the bit order and waveform shape in both time and amplitude. hence the above data byte would be transmitted as (01011100). a high level is called a Mark state. In normal operation. b7. At the start of each timing period. For serial communication. and computers are equipped with a serial interface. often denoted as a 1. a 300 Baud data rate has a timing period of 1/300 of a second or 3. b0. © National Instruments Corporation 11-1 Fundamentals of Digital Electronics .
a serial transmitter can be designed using a 10-bit shift register and a delay loop that simulates the Baud rate. b0 b7 Start 0 0 1 0 1 1 1 0 0 1 Stop Figure 11-4. the data comes out in the reverse order. the start bit (Space state) and the Stop bit (Mark state). However. Figure 11-5. Launch the VI Serial. Hence. In terms of a timing diagram. with the least Fundamentals of Digital Electronics 11-2 © National Instruments Corporation . the RS-232 serial waveform for the $3A data byte looks like the following. Serial Waveform for a $3A Data Byte Serial Transmitter In LabVIEW. If each byte represents one ASCII character. $33 is entered as (0011 0011). Serial Transmitter Sends the LSB (b0) First The protocol also requires that the data byte be framed by two special bits.vi. Handshaking Bits Start and Stop Frame the Data Byte The addition of these framing bits requires 10 timing periods to send one data byte. Note that the bit order in hexadecimal places the most significant bit on the left. Start 0 bit b0 b7 0 1 0 1 1 1 0 0 data byte $3A Stop 1 bit Figure 11-3.Lab 11 Serial Communications 8-bit data $3A b0 b7 0 1 0 1 1 1 0 0 Figure 11-2. LabVIEW Simulation of a Serial Transmitter On the front panel. 10 serial bits are sent for each character. a 9600 Baud modem is capable of sending 960 characters per second. you can load the date byte into the shift register by operating the eight input switches. For example.
All data bits and framing bits are shown as zeros before execution. after 10 cycles. Serial1.vi. The output bit immediately falls to the off state.Lab 11 Serial Communications significant bit first. the next bit is output. Initially. Figure 11-6. signaling the start of transmission. the serial output is converted into a numeric and then written to a LabVIEW © National Instruments Corporation 11-3 Fundamentals of Digital Electronics . and the start bit becomes a 0. the shift register is filled with ones. As the data is shifted out the serial line. executes the loop 10 times. The following eight elements are the data byte in sequence. the stop bit becomes a 1. Transmitter Buffer After Data Byte Has Been Sent to the Port It becomes easier to view the serial waveforms by writing the serial output to an oscilloscope or a strip chart recorder. Figure 11-7. The diagram panel displays the transmitter algorithm. In the second VI. a Boolean False. As soon as the run button is pressed. least significant bit to most significant bit. The VI. A wait structure simulates the "basic timing period" or 1/Baud Rate. LabVIEW Diagram Panel for the Serial Transmitter Simulation The first bit to be output (Start) is initialized to the Space state (0). Each loop outputs one serial bit. This ensures the output will be in the Mark state at the end of transmission. The serial output is displayed on the large square LED indicator. when called. After a delay (1/Baud Rate). a Boolean True. $33 is loaded into the shift register. The last element on the shift register (Stop bit) is initialized to a Mark state (1). it is in the Mark state.
$55 (01010101). Fundamentals of Digital Electronics 11-4 © National Instruments Corporation . and you can view the transmitted serial waveforms at low baud rates. the trace will resemble that of an oscilloscope trace. By selecting the correct set of chart symbols and interpolation features. which in turn is passed on to the parallel-to-serial converter. converts the analog signal into an 8-bit binary number. Figure 11-8. and $FF (11111111). the serial waveform is passed into an array and presented on the front panel as a logic trace. this VI will have eight binary inputs for the input parallel data byte. the parallel-to-serial converter can be saved as a subVI and used in other programs. and a numeric array for the logic trace. RampADC. a binary output for the serial bit stream. discussed in Lab 9.Lab 11 Serial Communications chart.vi. generates a square wave on the serial output pin. Voltage to Serial Transmitter In the first application. The numeric value has been conditioned to be in the range 0-255. Serial Waveforms for Repetitive Transmission of the Same Data Byte Note the middle case. The following traces show the waveforms for the numbers $00 (00000000). Once built. In general. To observe the signal. $55. a numeric input simulates an analog input.
Serial Transmitter Exploits LabVIEW SubVIs Load the VI named V->Serial. Each number from 0 to 255 will yield a different waveform.vi.vi and observe the serial waveforms. $55.vi. Figure 11-10. which converts the hexadecimal characters into a number.vi (demonstration of a serial transmitter) Serial1. The numeric value is then passed on to the previous VI. $55 also generates the square wave.Lab 11 Serial Communications Figure 11-9.vi generated a square wave. even or odd. Waveform Generator with Hexadecimal Input The hexadecimal string value is converted into a numeric value using a LabVIEW string function called Format and Strip. LabVIEW Challenge Can you generalize this input to be any 7-bit ASCII character? The eighth bit could be a parity bit. Try the data bytes $00.vi (LabVIEW simulation of a serial transmitter) © National Instruments Corporation 11-5 Fundamentals of Digital Electronics . a two-character hexadecimal-encoded ASCII string is input into a subVI named Hex->Numeric. In the second example. and $FF to verify the waveforms shown in Figure 11-8.vi. V->Serial. and displayed. Lab 11 Library VIs (Listed in the Order Presented) • • • Serial. Recall that (0101 0101) in Serial1. In HEX->Serial.vi (Serial.vi with a logic trace output) V->Serial.
vi (subVI 8-bit DAC) FlipFlop.vi with numeric array output) Fundamentals of Digital Electronics 11-6 © National Instruments Corporation .vi (subVI that converts hexadecimal number into a numeric) Serial2.vi (subVI T flip-flop) Hex->Numeric.vi (subVI 8-bit binary counter) DAC.vi (LabVIEW simulation of a serial transmitter with hex input) RampADC.vi (subVI 8-bit ADC) Binary Counter.Lab 11 Serial Communications • • • • • • • Hex->Serial.vi (subVI Serial1.
It decides which data paths must be opened and closed to execute the instruction. and registers. An example of this type of instruction is "clear the accumulator. the instruction needs additional information. the instruction is executed by opening and closing various gates to allow execution of the instruction. © National Instruments Corporation 12-1 Fundamentals of Digital Electronics . Special memory locations called input/output (I/O) ports pass binary information to or from the real world in the form of parallel or serial data bytes. The CPU reaches out to this sequence by controlling and manipulating the address bus." In other cases.Lab 12 Central Processing Unit The heart of any computer is the central processing unit (CPU). The first part of the instruction is passed to the instruction decoder. including the arithmetic and logic unit (ALU). the instruction decoder. In a typical CPU sequence. data constants. An example of this type of instruction might be "load Register 2 with the data constant 5. all the information needed to complete the operation is embedded within the instruction. The CPU communicates with the memory over a bidirectional data bus. the program counter. I/O. memory. This lab illustrates how the CPU executes simple and a few complex operations using basic logic functions. such as clear. and clock). complement. In some cases. Typical instructions available to all CPUs include simple instructions with data already inside the CPU. This instruction is passed over the data bus to the internal registers. ensuring that all bits arrive on time at the right place and that no data trains collide. The system clock oversees the whole network of gates. the program counter reaches out to the memory via the address bus to retrieve the next instruction." Once all the information is in place. and it returns to memory for the added data. and a bank of internal memory cells called registers. all placed in an ordered sequence. and variables. The CPU consists of several subgroups. More complex instructions use two internal registers or data coming from memory. In memory reside program instructions. latches. Of the four parts of a computer (CPU. or increment the accumulator. the most important part is the CPU.
The OR operation sets all bits high in the output register.R2. or 32 bits. Data is entered into the input registers by clicking on the bar below each bit. The following are some elementary CPU operations. Investigate the above operations using ALU0. hence this operation is equivalent to COMPLEMENT Register 1. Fundamentals of Digital Electronics 12-2 © National Instruments Corporation . The AND operation resets the output register to all zeroes. OR. hence this operation is equivalent to SET OUTPUT. What operation does or AND R1[$00]. The type of instruction (AND. Figure 12-1. the registers R1 and R2 are represented by 1D arrays having Boolean controls for inputs. Running the program executes the selected logic function. OR. The third operation inverts the bits in R1. X is used to indicate any hexadecimal character.vi. Here. and for simplicity the results of an operation will be placed in a third register called Output. The output register is a Boolean array of indicators. R2[$FF] represent? In each case. ALU0. hence this operation is equivalent to CLEAR OUTPUT. This lab will focus on 8-bit CPUs.vi. or XOR) is selected with the slide bar control. LabVIEW Simulation of an Arithmetic and Logic Unit In the LabVIEW simulation. or XOR) is selected from the instruction mnemonic such as AND R1. 16. The function (AND. R2[$XX] XOR R1[$55].Lab 12 Central Processing Unit Operation of the Arithmetic and Logic Unit The arithmetic and logic unit (ALU) is a set of programmable two-input logic gates that operate on parallel bit data of width 4. the data to be entered is included inside the [ ] brackets as a hexadecimal number such as $F3. R2[$XX] OR R1[$FF]. 8. The input registers will be called Register 1 and Register 2.
the second input register.Lab 12 Central Processing Unit Consider the operation "Load the Output Register with the contents contained in R1.vi to some known value and execute the operation AND R1. and the CPU operation is complete.. is connected to the output register so that the output becomes the input for the next operation. each bit (0. It should now be clear from these few examples that many CPU operations that have specific meaning within a software context are executed within the CPU using the basic gates introduced in Lab 1." Set R1 in ALU0. as this task can be done automatically by disabling indexing at the For Loop tunnels. then executing the ALU operation on that bit. it is not necessary to strip off each bit. © National Instruments Corporation 12-3 Fundamentals of Digital Electronics .R1. provides another common task. This structure provides a much-simplified CPU structure. The Accumulator In ALU0.vi.R2[$FF]. R2..7) has passed through the ALU." In a text-based programming language. XOR R1. Study carefully the following example. but more importantly. The result is passed on to the output array at the same index with Replace Array Element. this operation might read "Output = Register 1. which uses this LabVIEW feature. CLEAR R1. the output register automatically becomes an accumulator. Another interesting combination. CPU operations are executed by stripping off one bit at a time using the Index Array function. Figure 12-2. Array data paths are thick lines. In many CPUs. LabVIEW VI to Simulate the Operation of an 8-Bit ALU In LabVIEW. After eight loops. but become thin lines for a single data path inside the loop.
Figure 12-4. Load and run the VI.vi. Addition The ALU not only executes logic operations. Load A with 5. This programming style allows individual CPU instructions to be executed in sequence. is accomplished with the AND function and a mask of (1111 1111). but also the arithmetic operations. The complement of A appears in the label Accumulator*. Fundamentals of Digital Electronics 12-4 © National Instruments Corporation . these two functions can be wired as a half adder (that is. The full adder shown below adds the two input bits plus a previous carry using the Boolean shift register. Together. and the next accumulator value is output on the right. ALU Simulation Uses the Auto Indexing at the For Loop Tunnels In ALU1.vi adds addition to the ALU operations. a full adder is used. and the mask $FF into R1. Look at the following example. Recall from Lab 3 that binary addition adds the individual bits using the XOR function and calculates any carry with an AND function. to see the operations.vi. Load A with 5 then Complement A. which sums the two input bits plus any carry from the previous bit place. LabVIEW VI to Load A with 5 Then Complement A The first instruction.Lab 12 Central Processing Unit Figure 12-3. bit 1 + bit 2 = a sum + a carry (if any)). The binary value for 5 (0000 0101) is placed into the initialization register. To propagate bit addition to the next bit place. ANDing these registers loads R1 with 5 and places its value into the accumulator. A new instruction. The VI named ADD_c. the previous accumulator value is input on the left. Complement is the XOR function with a mask of $FF. Prgm1.
the program might read Start Loop CLEAR A INCA REPEAT Loop N : reset all bits in the accumulator to zero : add +1 to accumulator : repeat last instruction n times ANDing a register with $00 will reset that register. add one to the accumulator again and again" for n times. the AND operation is case number 1. CPU operation number 3. In a linear programming language. LabVIEW VI of an 8-Bit Binary Counter Note that the carry has not been wired.Lab 12 Central Processing Unit {ADD +1. It might be coded as "after clearing the accumulator. The simulation VI is shown below.A}. Figure 12-5. By wiring the carry. ALU Operation: ADD with Carry Binary Counter Consider a software program to generate the binary patterns of an 8-bit binary counter. can now be added to the list of operations and added to the Case structure. the instruction would correctly be © National Instruments Corporation 12-5 Fundamentals of Digital Electronics . In the CPU list of instructions.A instruction. INC A is the ADD +1. The INCREMENT instruction does not affect the carry. CLEAR A. Figure 12-6.
AND.Lab 12 Central Processing Unit written as ADD +1. OR. XOR.vi.vi (ALU simulation with AND. Figure 12-7. Front Panel for a LabVIEW Simulation of an 8-Bit Binary Counter LabVIEW Challenge Design a LabVIEW program to simulate the addition of two 16-bit numbers.vi (ALU simulation with concise programming format) ADD_c. complement A) Prgm2.A. Prgm2.OR.vi (subVI used in CPU add operation) Fundamentals of Digital Electronics 12-6 © National Instruments Corporation .vi (LabVIEW CPU simulation of a binary counter: clear A. and ADD operations) Prgm1. and XOR) ALU1.vi (subVI used in CPU add operation) Full Adder. A Wait loop has been added so that the user can easily see the action as the VI is run. Load and run the simulation VI. Lab 12 Library VIs (Listed in the Order Presented) • • • • • • • ALU0. ADD 1 to A) Half Adder.vi (LabVIEW simulation arithmetic and logic unit. and watch yet again the binary counter.vi (LabVIEW CPU simulation: load A with 5.
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