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A high fidelity hearing aid is disclosed for providing high quality sound and is primarily directed to those users whose hearing loss is such that they need some amplification for low level signals, but do not need amplification for high level signals.
1. A high fidelity head-worn hearing aid including microphone means for receiving an audio input signal and converting said audio signal to an electrical signal, variable gain amplifier and gain control circuitry receiving said electrical signal from the microphone, receiver means for receiving the electrical signal from said amplifier circuitry and converting said electrical signal to an audio signal, means for coupling said audio signal from the receiver to the ear of the user, low voltage power supply means for providing electrical power to energize said microphone means, said receiver means and said amplifier and gain control circuitry, a feedback path in said amplifier circuitry, a voltage controlled resistance means in said feedback path, logarithmic amplifier circuit means responding to the electrical signal from said microphone and providing a voltage to said voltage controlled resistance having a logarithmic relationship over a selected intermediate input signal levels and a deviation toward linear operation at higher input signal levels for providing a selected response to the intermediate input signals and a rapid decrease in the voltage provided to the voltage controlled resistance at the upper threshold of compression whereby the voltage controlled resistance means will have negligible effect on the operation of the amplifier circuitry at high signal levels and a low distortion, low noise, selected compression ratio amplifier circuitry is provided for said hearing aid.
2. A structure as in claim 1 wherein the voltage controlled resistance is effective in the circuit from below 30 up to 90 dB SPL and then becomes substantially ineffective at levels about 90 dB SPL.
3. A circuit as in claim 1 wherein the output of said logarithmic amplifier is controllable to provide a variable compression ratio.
4. A circuit as in claim 1 wherein said circuitry provides a fixed compression ratio control.
5. A circuit as in claim 1 wherein said voltage controlled resistance element is a transistor connected in grounded emitter configuration.
6. In a hearing aid, an amplifier circuit having a feedback means, a voltage controlled impedance in said feedback means, means for varying the impedance of said voltage controlled impedance in a logarithmic relation with respect to the amplitude of said output within a selected intermediate range and means for causing said impedance to have negligible effect on the operation of the circuit above selected signal levels whereby signals of low range of intensity are amplified more than signals of an intermediate range of intensity, and signals above said selected signal level obtain constant gain to thereby provide a low distortion, low noise variable compression ratio circuit.
7. A hearing aid as in claim 6 wherein voltage controlled impedance comprises a transistor, said voltage controlled impedance provides an effective amplification up to a selected level, and means for functionally disconnecting said transistor from the circuit whereby said circuit provides constant gain above said selected signal level.
8. A circuit as in claim 6 wherein said low range is from 0 to 20 dB; said intermediate range is from 20 to 80 dB and said upper range is above the level of 80 dB, all dB relative to 1 microvolt.
9. A circuit as in claim 6 further including switch means for selectively by-passing said voltage controlled resistance for changing the circuit from a linear amplifier to a selected compression ratio amplifier.
10. A high fidelity head-worn hearing aid including microphone means, variable gain amplifier and gain control circuitry for receiving a signal from the microphone, receiver means, a feedback path in said amplifier circuitry, a voltage controlled resistance means in said feedback path, a logarithmic amplifier circuit for providing a voltage to said voltage controlled resistance means having a logarithmic relationship over selected intermediate audio input signal levels, and means for increasing the resistance of said voltage controlled resistance means, the resistance of said voltage controlled resistance means being increased significantly above a selected signal level whereby the voltage controlled resistance means will be effective at the lower and intermediate signal levels and have negligible effect on the operation of the circuit at high signal levels whereby said amplifier circuitry provides amplification of the signal according to logarithmic relation up to a selected level and linear operation above said selected signal level to thereby provide a low distortion, low noise amplifier circuitry having a selected compression ratio.
11. A circuit as in claim 10 further including a field effect transistor to further attenuate high sound level outputs from the microphone.
12. A high fidelity hearing aid including a low power consumption automatic gain control amplifier suitable for operation with a miniature battery such as used with head-worn hearing aids, said automatic gain control amplifier providing automatic gain control for inputs between a fixed lower threshold voltage and a fixed upper threshold voltage and with a low distortion, fixed gain operation of the amplifier for inputs above the upper threshold and for inputs below the lower threshold.
13. An automatic gain control circuit including a feedback subcircuit, a voltage controlled impedance means comprising at least one solid state element in said feedback subcircuit, said voltage controlled impedance means providing a variable impedance up to a selected high signal level, said feedback subcircuit effecting a variable gain determined by said voltage controlled impedance means, a logarithmic amplifier means, means for rectifying the output of said logarithmic amplifier and coupling said output from said rectifying means to said solid state element to cause said element to be sensibly non-conducting above said selected signal level for increasing the impedance of said voltage controlled impedance for signals above said selected signal level to cause said voltage controlled impedance means to have negligible effect on said gain control circuit above said high signal level, whereby said automatic gain control circuit provides a preselected gain up to said signal level and essentially constant gain above said signal level and thereby obtains a low noise, variable gain amplifier circuit with low distortion at high signal levels.
Certain users of hearing aids have a mild to moderate loss of normal sensitivity for low intensity sounds, but retain excellent speech discrimination capabilities and good sound quality judgment capabilities for sounds which are intense enough to be audible to them. This phenomena, commonly referred to as loudness recruitment was, for example, discussed by Steinberg and Gardner in "The Dependence of Hearing Impairment on Sound Intensity", Journal of the Acoustical Society of America, Vol. 9, Pages 11-23 (1937). Accordingly, those hearing aid users who have a hearing impairment characterized by a mild to moderate loss of sensitivity for low intensity sounds require no amplification for high intensity sounds; and, amplification of high intensity sounds will generally cause them discomfort. This problem is well understood in the art, and a variety of solutions have heretofore been employed. However, most of the prior art solutions introduce deterioration in the quality of the delivered sound, so that traditional hearing aids have often been characterized as "low fidelity instruments".
One prior art approach has been to limit the saturation sound pressure output of the hearing aid by means fo a simple peak clipping, which produces large amounts of harmonic and intermodulation distortion. More recently, relatively low distortion compression limiting has been used to limit the saturation sound pressure output of the hearing aid without the introduction of large amounts of harmonic or intermodulation distortion. With either type of output limiting, the saturation sound pressure level out of the hearing aid can be set to a level somewhat below the discomfort level of the user. A typical input-output curve for an output limiting hearing aid is shown in FIG. 4. One disadvantage to the output-limiting approach is that a large percentage of the incoming sounds will be amplified to a point which is near the user's discomfort level.
Another prior art approach has been to use an automatic volume control (AVC) circuit which acts to produce a nearly constant output level for a wide range of input sound pressure levels. In this case, the nearly constant output level can be set to the user's most comfortable listening level, so that the majority of useful sounds are presented at the most comfortable listening level for the user. A typical input-output curve for an automatic volume control hearing aid is shown in FIG. 4. A problem with this latter approach is that the normal dynamic range of the desired sounds is unduly reduced at the output, so that quiet input sounds and background noises are amplified until they appear nearly as loud to the user as loud input sounds. This excessive reduction of the dynamic range lends an unnatural quality to the sound.
A more sophisticated solution provided by the prior art has been the use of wide dynamic range compression amplification wherein the overall gain of the hearing aid is changed smoothly and continuously from a maximum value for low level inputs to a minimum value for high level inputs. Compression hearing aid amplifiers are commercially available which have a nearly constant compression ratio of 2:1 over an input dynamic range of 60 dB or more. With a 2:1 compression ratio, for example, such 10 dB increase in input level causes only a 5 dB increase in output level. An early version of such a compression amplifier suitable for hearing aids was described in U.S. Pat. No. 3,229,049, issued to Hyman Goldberg on Jan. 11, 1966. A typical input-output curve for prior art logarithmic compression hearing aids is shown in FIG. 4. A drawback to such prior art devices, however, is that they provide a compression function characterized by an essentially constant compression ratio for all sound levels up to those sufficiently intense to cause overload of the input circuit, which commonly occurs at microphone input levels corresponding to a hearing level of approximately 80 dB (input sound pressure levels of 90 to 95 dB). For sounds whose sound pressure level exceeds 90 to 95 dB, the overload of the input circuitry causes a rapid increase in amplifier distortion. Since sounds whose peak levels exceed 90 to 95 dB are commonly encountered at concerts, social gatherings, etc., the high distortion levels of such prior art amplifiers renders them unsuitable for use in a high fidelity hearing aid.
Also high quality compression circuits or systems for use in broadcast and recording studio applications are known in the art, see, for example, U.S. Pat. Nos. 3,681,618 and 3,714,462, both to David Blackmer. In these latter systems, the compression ratio and the lower and upper threshold of compression can be readily adjusted by the user to optimize the overall sound quality with different program materials. Such prior art systems have generally required power supply voltages and currents which would be impractical in a head-worn hearing aid; more specifically, power supply requirements of plus and minus 12 volts at a total current drain of 10 mA or more is not uncommon for such prior art systems.
Accordingly, it is a principal object of the present invention to provide a high fidelity hearing aid.
It is another object of the present invention to provide a very low noise, low distortion, variable gain preamplifier capable of handling the unattenuated output of a subminiature microphone without distortion for input sound pressure levels of 110 dB SPL or greater.
It is another object of the present invention to provide a low distortion, low noise, variable compression ratio circuit which requires a supply voltage of 1.5 volts, or less, and a supply current of approximately 100 microamperes, or less.
It is a further object of the present invention to provide a preamplifier whose gain in dB is linearly related to the logarithm of the output signal voltage over an input range of at least 40 dB.
It is yet another object of the present invention to provide a preamplifier circuit with the compression ratio and the maximum gain of the preamplifier adjustable by the user in a simple manner without affecting the ability of the circuit to provide low distortion operation.
A further object of the present invention is to provide a circuit for obtaining wide dynamic range logarithmic compression acting to increase circuit gain for low level signals, in combination with fast-acting, low distortion output limiting compression acting to attenuate the microphone output when output SPL's exceed some predetermined level, and wherein the two separate compression actions do not interact in an undesirable manner.
These and other such objects as may hereinafter appear are attained in the embodiments of the invention shown in the accompanying drawings wherein:
FIG. 1 shows a high fidelity hearing aid incorporating the inventive circuit in accordance with the invention;
FIG. 2 shows certain circuits for interfacing the inventive circuit with the microphone and receiver of the hearing aid of FIG. 1;
FIG. 3 shows the inventive circuit for providing a continuous range of compression ratio adjustment from 1:1 to 4:1;
FIG. 4 is a group of input-output curves obtained with various prior art circuits as compared to the desirable type of input-output curves and all of said circuits compared with unity gain curve;
The curves of FIGS. 4, 5, 6 and 8 have been labeled fully for ease of understanding.
FIG. 5 is a family of curves obtained with various compression ratio adjustments of the circuit of FIG. 3;
FIG. 6 is a total harmonic distortion curve of the circuit of FIG. 3 as adjusted for a 2:1 compression ratio;
FIG. 7 is a relatively simplified embodiment of the circuit of FIG. 3 which provides a fixed compression ratio; and,
FIG. 8 shows a family of curves obtained with the various settings of the control of the circuit of FIG. 7.
As discussed above, many users with a mild to moderate hearing loss experience essentially normal loudness sensation for sounds above a certain intensity level. Examination of clinical data and the literature indicates that recruitment is typically complete, that is, the loudness sensation is essentially normal, for sounds corresponding to a hearing level of 80 dB or greater. Consider that for speech sounds, an 80 dB hearing level corresponds to a sound pressure level (SPL) in the sound field of approximately 95 dB; and for pure tones, 80 dB hearing level corresponds to approximately 80 to 90 dB SPL in the sound field in the frequency range important for speech perception.
For a minimum degradation in the perceived sound quality, a high fidelity hearing aid should provide sensibly unity acoustical gain over that range of sound intensities in which the user has essentially normal loudness sensations. An ideal high fidelity hearing aid should thus not overload for input sounds above 90 dB SPL, but should produce unity acoustical gain up to the 105 to 115 dB peak sound pressure levels commonly encountered at concerts, social gatherings, etc.
Consider now the low level input-output characteristics required of a high fidelity hearing aid. A gain numerically equal to the user's hearing loss would be required to restore his threshold down to audiometric zero levels; however, such a large amount of gain is commonly found to be unacceptable. A reason for the foregoing is that under most circumstances, the masking produced by the background noise levels commonly encountered in residences, offices, etc. render even those persons with unusually acute hearing incapable of detecting sounds which are less than 15 to 30 dB above commonly accepted audiometric zero levels. Similarly, the upper limit of what is commonly accepted as the range of normal hearing is set at 25 dB above audiometric zero levels. Thus a maximum amplification sufficient to reduce the hearing loss to 15 to 20 dB has been generally found appropriate.
It is readily seen, therefore, that a high fidelity hearing aid designed for minimum degradation in perceived sound quality should typically have a gain-versus-input level which is characterized by a maximum gain which is 15 to 20 dB less than the hearing loss, and is constant for inputs below a 15 to 20 dB hearing levels. Further, such a high fidelity hearing aid should have a gain which decreases smoothly as the input is increased in the range from the 20 dB to 80 dB hearing levels, and has a constant gain of unity (0 dB acoustic amplification) for sounds above the 80 dB hearing level. In practice, it is also generally desirable for the hearing aid to incorporate fast-acting low distortion compression limiting applied to the microphone output for sounds above the 100 dB hearing level (110 to 115 dB SPL). This latter function not only prevents occasional uncomfortably loud sounds from reaching the user, but also functions to avoid any distortion or bias shifts in the amplifier during such sound extremes. An example of the desired gain-versus-input level characteristic discussed above is illustrated in FIG. 4 for an individual with a 45 dB hearing loss. The inflections of "knees" occurring at points B and C in the curve of FIG. 4 will hereafter be respectively referred to as the lower and upper thresholds of compression.
In a hearing aid, a variable compression ratio control is also desirable so that one basic hearing aid design can cover a wide variety of hearing losses in the mild to moderate range and yet, in each individual case, provide the minimum compression ratio required in order for the user to have adequate gain for very low level signals. Moreover, if controls for adjustment of compression ratio are made available, the user can reduce the compression ratio and thus the gain for moderate-level signals when he finds himself in a noisy environment so the environmental noises are not amplified annoyingly. Being able to chose the minimum compression ratio appropriate to each situation is desirable because it generally provides the best overall sound quality.
Experiments using commonly employed speech tests, for example, have shown that 2:1 compression ratio with the characteristics shown in FIG. 4 will provide adequate gain to compensate for a 45 dB hearing loss, and will reduce the 45 dB hearing loss down to approximately 15 dB, which is essentially in the normal range. At the same time, such a 2:1 compression ratio is low enough so that its operation is frequently unobtrusive enough to be nearly inaudible to the untrained listener with normal hearing. For example, in the course of conducting various experiments it was found that when the inventive circuit is inserted in the amplification chain of a home high fidelity system, it makes it possible to enjoy wide dynamic range classical recorded music at comfortable listening levels without the annoyance created when portions of the music drop below audibility due to the masking produced by the noise of household appliances. With the appliances turned off, moreover, casual listeners who have been asked to judge the overall sound quality of the system have, with rare exception, not even noticed the presence of the signal processing provided by the 2:1 compression circuitry.
The applicant believes that the combination of the desirable features discussed above in a low power, low noise circuit suitable for use in head-worn hearing aids is new in the art. More particularly, the inventive circuit provides low distortion, low noise, variable compression ratio operation while requiring a supply voltage of only 1.5 v or less and consuming approximately 100 microamperes of supply current. The circuit disclosed herein provides less than a 1.5 micro volt input noise level with various setting of the compression ratio including a setting of 1:1 which corresponds to a fixed gain or unity gain condition, while introducting a total harmonic distortion of 2%, or less, for any input signal voltage between 1 micro volt and 60 millivolts rms and for any compression ratio setting between 1:1 and 3:1. The present circuits produce a total harmonic distortion below 5% even with an input signal voltage as high as 100 millivolts. Thus, it is seen that the present circuit provides an undistorted input dynamic range, that is, the range between the input noise level and the input overload level, of nearly 100 dB.
FIG. 1 is a view partly in cross section of a high fidelity hearing aid 10 in accordance with the invention. As will be appreciated, the structure of the high fidelity hearing aid 10 may include the usual microphone, receiver and battery mounted in the hearing aid housing. The hearing aid 10 may include acoustic damping elements in the conduit coupling the output of the receiver to the ear mold and thence to the ear of the user. High fidelity hearing aid 10 also includes complete amplifier 12 as shown in FIG. 2, which includes the variable compression ratio amplifier 11 in accordance with the invention which is shown in more detail in FIG. 3.
FIG. 2 shows the complete amplifier circuitry 12 for adapting or interfacing the inventive circuit with the microphone and receiver of the high fidelity hearing aid 10, as will be described more fully hereinbelow.
Refer now to FIG. 3 which shows a schematic diagram of a preferred embodiment of the invention. A listing of the values of the various components or elements of the circuit 11 of FIG. 3 follows the description of the operation of the circuit.
In FIG. 3, a signal ein as from a microphone is coupled through a series connected capacitor C2 to an amplifier 30 comprising transistors Q1 and Q2. An important feature of circuit 11 is the feedback network provided by resistors R6 and R7 and transistor Q4 connected in an inverted configuration to provide an impedance in the feedback circuit configured as a voltage controlled resistance (VCR) element.
A brief explanation of the function of the VCR in the inventive circuit 11 is now in order. In the desired range of operation, the AC resistance of the VCR transistor goes from a few hundred ohms to over 1 megohm and the resistance is an approximately inverse exponential function of the control voltage. A small signal AC resistance of about 100,000 ohms associated with the DC control voltage of 400 mV, with a 10-fold decrease in AC resistance resulting from each 60 mV increase in control voltage, is typical of some devices. This predictable inverse exponential control characteristic allows a simple implementation of a logarithmic compression gain control function, as is well known.
In the circuit of FIG. 3, the VCR transistor is placed in shunt with resistor R7 for AC currents by means of the coupling provided by low impedance capacitor C3. When the AC resistance of the VCR is high (1 megohm for example), its shunting effect on R7 will be minimal and so the gain of amplifier 30 will be determined by the values of feedback resistors R6 and R7. In the preferred embodiment, R6 and R7 are equal valued resistances, and the voltage gain of amplifier 30 is approximately 6 dB under these conditions. When the AC resistance of the VCR is low (a few hundred ohms, for example), on the other hand, its shunting effect on R7 will be maximal and the gain of amplifier 30 will be maximum. In the preferred embodiment, a maximum gain for amplifier 30 of about 46 dB is obtained with a control voltage of approximately 600 mV applied to the VCR transistor Q4.
It has been found that the nonlinearity of such a VCR element tends to introduce undesirable distortion as the AC voltage is increased, see FIG. 6. With a 1.5 mV rms AC sine wave, for example, a 1.5% total harmonic distortion results, which is about the upper limit for a high fidelity instrument. Accordingly, to maintain a low distortion, the AC signal could be limited to a maximum 1.5 millivolts across the voltage controlled resistance (VCR) when the VCR is a controlling resistance in the circuit operation. A disadvantage to this approach in a hearing aid, is that if the microphone output level is attenuated by the 32 dB required to bring the 60 mV (110 dB SPL equivalent) levels down to 1.5 mV, the intrinsic noise level of the circuitry will become objectionable with low level inputs. It is, therefore, not advisable to substantially lower the microphone level and subsequently amplify it after coupling to the VCR. In order to redude the deleterious effect of preamplifier noise levels, it is desirable to obtain the highest possible signal voltage levels out of the microphone, but in order to reduce the deleterious effect of nonlinear distortion at high levels, it is desirable to attenuate the signal voltage levels applied to the VCR.
The inventive circuit 11 provides a solution to the foregoing problem by biasing the nonlinear voltage controlled resistance (VCR) element into a sensibly nonconducting state under high input signal level conditions, and bringing the VCR into effective operation only under low level input conditions. Thus under high input signal voltage conditions, where the nonlinearity of the VCR transistor Q4 becomes evident, only a negligable portion of the signal current flows through VCR transistor Q4 while the main port of the signal current flows through (linear) resistor R7. Thus, the large signal nonlinearity of the VCR has only a negligable effect on the operation of amplifier 30. Furthermore, a maximum of negative feedback is applied around amplifier 30 under high signal level conditions so as to further minimize the effect of the nonlinearities in the amplifier transistors Q1 and Q2. Under low input signal voltage conditions, on the other hand, the operation of transistors Q1 and Q2 and the AC resistance of VCR transistors Q4 are all sensibly linear, so that undistorted operation of amplifier 30 is obtained even under maximum gain conditions (i.e., even when the shunting effect of transistor Q4 on feedback resistor R7 is maximal). With this approach, an undistorted dynamic range improvement of 30 dB or more may be obtained over that obtained when the VCR remains the controlling element at all signal levels as shown in FIG. 6. Note in FIG. 6 that the distortion of circuit 11 is 1% or less for AC inputs up to 30 mV, and less than 5% with 100 mV inputs. Careful listening tests indicate that the amount of harmonic distortion introduced by the operation of circuit 11 (and illustrated in FIG. 6) is undetectable, even to a trained listener, under most listening conditions.
Return now to the description of the circuit of FIG. 3. The signal from amplifier 30 is coupled from transistor Q2 to an AC buffer amplifier 32 comprising transistor Q3 and resistor R8. The emitter of transistor Q3 is coupled through capacitor C4 and resistor R9 to the base of transistor Q5 of logarithmic amplifier 34 to provide a low impedance drive voltage for the amplifier 34. The logarithmic amplifier 34 includes transistors Q13, Q5, Q6, Q7 and diodes D1, D2 and D3. The emitter of transistor Q3 also couples an output to the amplifier of the associated hearing aid or other device as indicated.
The logarithmic AC amplifier 34 has a very high input impedance and roughly 60 dB of open loop gain. The diode D1 connected in parallel with diodes D2 and D3 and resistor R13 functions as a nonlinear feedback impedance which in cooperation with the input resistor R9 provides a closed loop gain which is related to the input signal voltage ein in such a way that the peak voltage at the collector of Q7 is proportional to the logarithm of the peak AC voltage ek developed at the junction 14 of the capacitor C4 and resistor R9. The voltage at the collector of Q7 will have a DC resting value of roughly 850 mV DC with an AC input of 0.3 mV or less and a negative going AC peak value which increases logarithmically at a rate of approximately 220 mV for each factor of ten increases in input signal voltage ek.
With low values of resistor R13, this nearly exact logarithmic relationship exists over a 60 dB range of AC input voltages ek extending from a 0.3 mV to 300 mV. With higher values of resistor R13, a deviation toward linear operation is obtained at higher input levels. The foregoing deviation makes possible a more rapid decrease in control voltage to the VCR once the upper threshold of compression has been reached in order that the nonlinear VCR will have neglible effect on the operation of the circuit 11 at high signal levels.
The sum of the base emitter offset voltages of Q5 and Q7 produces a relatively high DC input voltage so that two series diodes (D2 and D3) rather than one may be used in the feedback loop without incurring the undesirable negative voltage clipping which would otherwise occur due to saturation of transistor Q7. The high sensitivity of the logarithmic amplifier 34 in turn allows a relatively high compression ratio without the need for additional amplification of the control voltage. A wide range of operation combined with a high (220 mV/decade) sensitivity of the logarithmic amplifier 34 is thus made possible for operation with a 1.3 to 1.6 volt supply.
Diode D1 periodically applies an opposite polarity feedback current to that which periodically flows through diodes D2 and D3 in order to prevent a net DC current flow through capacitor C4 which would otherwise produce an undesirable shift in operating bias levels of the logarithmic AC amplifier as the input signal changes from a low to a high level.
Transistor Q8, resistor R17 and capacitor C5 provide a peak detection rectifier 35. Transistor Q8 is used in order to provide a high input impedance so the rectifier 35 does not load down the output of the logarithmic AC amplifier 34. Resistor R17 and capacitor C5 determine the attack and release time of the circuit 11 which, in the embodiment shown, has an attack time of 3 milliseconds and a release time of about 50 milliseconds.
The compression ratio control potentiometer R19 is adjustable to couple a selected portion of the output voltage from the emitter of Q8 in rectifier circuit 35 to the DC buffer amplifier 36 whose output in turn provides the feedback control voltage applied to VCR transistor Q4. The lower terminal of potentiometer R19 is connected to the junction of resistor R18 and transistor Q11. Resistor R18 has its other terminal connected to supply potential, and transistor Q11 is connected through transistor Q12 to ground reference. Accordingly, resistor R19 may be adjusted so that a reference voltage VR, which is sensibly independent of the rectifier output voltage VC at the emitter of transistor Q8 is coupled through the buffer amplifier 36 to transistor Q4. The reference voltage VR is adjusted to be equal to the DC voltage obtained at the rectifier output when the input signal voltage is equal to the upper compression threshold value. Transistors Q11 and Q12 are preferably chosen to match the characteristics of transistors Q9 and transistor Q4 so that a temperature independent operation may be obtained.
The DC buffer amplifier 36 is formed by transistors Q9 and Q10 and the associated resistors provide a high input impedance, low output impedance, sensibly unity gain amplifier. Buffer amplifier 36 has a DC offset voltage which compensates for the DC offset voltage introduced by rectifier 35. The proper level of the DC control voltage VC is obtained by choice of resistor R16, which can also easily compensate for small differences in these offset voltages.
With the circuit valves listed hereinafter, the circuit of FIG. 3 will provide a maximum compression ratio of nearly 5:1. If a maximum compression ratio of only 3:1 is required, transistor Q10 and resistor R21 may be eliminated from the circuit, and buffer amplifier 36 will have noticeably less than unity gain, thus reducing the maximum compression ratio available in the circuit. Similarly, D1 D2 and D3 may be nongold-doped diodes such as formed by transistors Q11 and Q12 (connected as diodes) when a maximum compression ratio of less than 5:1 is acceptable; in such case it has been found desirable to insert a series resistor at the point labeled RX adjacent resistor R13.
In general, choosing a lower value for the upper threshold of compression will result in reduced distortion at all signal levels. Lowering the upper threshold of compression in the circuit of FIG. 3 or FIG. 7 may be accomplished most easily by reducing the value of R9 and/or increasing the value of R16, followed by appropriate selection of R13 and R18. Conversely, increasing the upper threshold of compression may be accomplished, at the expense of increased distortion levels, by increasing the value of R9 and/or reducing the value of R16.
As mentioned above, transistor Q4 is connected as a voltage controlled resistance VCR. The control voltage from buffer amplifier 36 is impressed across the base to collector junction of transistor Q4. The offset voltage developed across the emitter collector junction in this inverted connection is in the fractional millivolt region and is sensibly unchanging over the range of control voltages which is required to give 40 dB of gain control. An advantage of the low and sensibly unchanging offset voltage is that the control voltage is not mixed in with the signal voltage, so that as the control voltage is changed, it does not introduce any unwanted AC signal resulting in audible "clicks" or "thumps" in the output.
The circuit of FIG. 2 also shows an optional FET Q0 in shunt with the microphone output terminal. Note that resistor R2 may not be required in those cases where the microphone output impedance is itself high enough. The FET Q0 can be used to attenuate the microphone output when the sound level input to the microphone is so high that the linear output capabilities of the amplifier would otherwise be exceeded or the sound pressure level delivered to the user would otherwise be uncomfortable. For example, with a typical hearing aid receiver driven from a Class A output stange, the upper limit of linear operations of the Class A output stange may correspond to 110 dB SPL. Moreover, low current drain hearing aids often reproduce an undistorted output only up to 105 dB SPL or less. Even though the circuit of FIG. 2 will handle up to the equivalent of 115 dB SPL input, therefore, the associated output amplifier of the hearing aid would distort the signal under those input SPL conditions unless some means such as Q0 were provided to reduce the signal reaching the output amplifier. The AC voltage developed at the amplifier output may be sensed (by means such as shown in FIG. 2), and used to control the AC resistance of Q0 in such a manner as to prevent the above-described difficulties of output amplifier distortion and/or user discomfort. Since the input levels at which such operation will occur are substantially above the upper threshold of compression for the logarithmic compression circuit, undesirable interaction between the two circuit functions is avoided.
The value of capacitor C3 given hereinbelow is chosen so that the frequency response of the preamplifier will be sensible independent of gain over the audio band. By choosing a smaller value for C3, the frequency response will be dependent upon the input signal levels such that the gain and frequency response will be related to the input signal voltage in a continuous manner over a wide range of output levels due to the wide range logarithmic compression operation of the preamplifier. For example, in the circuit shown it has been found that a value for C3 which is 0.05 uf will often provide improved discrimination of speech signals in a background of noise, expecially when the noise has strong low frequency components. Capacitor C3 could be selected, or switched in and out of the circuit, to provide best sound quality for music, or best discrimination as for speech. Such level dependent variation of the frequency response is known in the art such as shown in U.S. Pat. No. 3,764,745 issued to Bottcher and Heyne; however, the combination with an amplifier providing automatic gain control for inputs between a fixed lower threshold and a fixed upper threshold, with low distortion constant gain operation for inputs above and below the threshold, has been hitherto unknown in the hearing aid art. Capacitor C4 may also be chosen to provide a frequency dependent operation of the VCR control voltage circuit with again the advantage that the operation is continuous over a wide output dynamic range due to the wide range logarithmic compression characteristic of the present circuit.
The input-output characteristics obtained with the circuit of FIG. 3 is shown in FIG. 5 for various settings of the compression ratio control potentiometer R19. Note in FIG. 5 that the lower threshold of compression, which occurs at an input signal voltage of approximately 10 microvolts, and the upper threshold of compression, which occurs at an input signal voltage of approximately 10 millivolts, are both sensibly unaffected by the setting of the compression ratio control potentiometer. Moreover, the maximum gain provided by the circuit 11 is automatically determined by the setting of the compression ratio control potentiometer so that a high compression ratio is accompanied by a high maximum preamplifier gain, and a low compression ratio is accompanied by a low maximum preamplifier gain.
In a hearing aid with commonly available electret or subminiature microphones, the lower threshold of compression corresponds to a hearing level of approximately 20 dB, while the upper threshold of compression corresponds to a hearing level of approximately 80 dB, see FIG. 4. Thus, it is seen from an analysis of FIGS. 4 and 5, that when used in a hearing aid, the circuit 11 can provide a constant maximum gain for sounds below approximately 20 dB hearing level, which sounds are typically composed largely of background noises; a smoothly decreasing gain with increasing sound intensity up to sounds corresponding to an 80 dB hearing level, and then a constant gain which may be chosen as unity acoustical gain by the proper selection of output amplifiers in the hearing aid, for sounds above 80 dB hearing level. Applicant believes that this highly desirable operation has hitherto been unavailable in any head-worn hearing aid.
FIG. 2 shows an application or connection of the inventive circuit in an overall hearing aid circuit. Resistor RB is chosen to produce the desired DC bias in the output transistor QT. Resistor RE may be chosen to produce the desired overall hearing aid gain levels; for example, RE may be chosen to produce unity acoustical gain in the hearing aid for sounds above approximately 80 dB hearing level, as discussed above. Resistor RF and capacitor CF are chosen to provide the desired output limiting as discussed above. Capacitor CR is used to control the high frequency response of the hearing aid and to insure amplifier stability. User operated potentiometer R19 controls the compression ratio in the 20 dB to 80 dB range of input hearing levels, as described above. An optional resistor R23 as shown in FIG. 3 may be used to limit the maximum gain of amplifier 11 by placing a resistance in series with VCR transistor Q4. A similar result may be obtained by increasing the value of resistor R20, thereby limiting the maximum control voltage available to VCR transistor Q4.
The circuit of FIG. 7 is a simplified version of the circuit of FIG. 3. In FIG. 7, a compression ratio of approximately 2:1 is all that is desired. Accordingly, transistor Q10, Q11 and Q12, and resistors R19 and R21 have been removed. Diode D3 has been moved from a position within the feedback loop as shown in FIG. 3, to a position where it provides a DC offset voltage in the output of the logarithmic AC amplifier. Resistors R15 and R16 are connected to form a voltage divider, with the value of resistor R16 chosen to produce the desired upper threshold of compression. A switch SW is provided and with switch SW open, resistor R23 functions somewhat like a volume control in the sense that it controls the maximum gain for low level signals. Its operation is illustrated in the curves of FIG. 8. With switch SW closed, the VCR is bypassed, so that the preamplifier 11 functions as a conventional linear amplifier with gain determined by the value of R23. It is thus possible to readily change back and forth from a conventional linear hearing aid to a wide range compression hearing aid in order to determine user preference for one type or the other in different listening situations.
It will be readily appreciated that in addition to application to hearing aids, the present circuitry will be useful in other applications where a large undistorted input dynamic range and a reduced output dynamic range are desirable. The use of low distortion wide range compression circuits is now commonplace in the recording industry, for example, as a means for reducing the effect of the noise level inherent to the recording medium. Use of such circuits has increased the quality of professional tape recorded program material. However, prior art low distortion wide dynamic range compression circuits suitable for such applications have been characterized by a power consumption which was too high to be suitable for use in miniature portable high quality tape recorders. Thus, the present circuit makes possible the application of previous automatic level control and noise reduction techniques to high quality miniature tape recorders without noticeably effecting their battery life. For such applications, it is possible to choose the circuit values to produce a maximum distortion of 1% or less throughout the entire dynamic range of the amplifiers.
While the invention has been particularly shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. For example, the basic circuit has been specifically designed for ease of translation into a monolithic integrated circuit.
Q1, q3, q4, q7, q9, q11, q12=high Beta NPN such as Motorola MMCS 930
Q5=super Beta NPN such as half of Intersil IT124/D monolithic dual
Q2, q6, q8, q10, q13--pnp such as Motorola MMCS5089 (Beta not critical in PNP transistors)
D1, d2, d3=gold doped silicon such as Motorola MMCD914
R4--1.4 meg
R5, r22--220k
R6, r7--56k
R8, r9--27k
R11, r12, r13--100k
R17--1 meg
R16--selected, approximately 10k
R18--selected, approximately 5 meg
R19--2.5 meg potentiometer
R21--2 meg
R23--optional, 100k variable
C2--0.01 uf
C3--1.0 uf
C4--0.05 uf
C5--0.33 uf
Patent Citations
Non-Patent Citations
Referenced by
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Abhyudaya Co-operative Bank Limited, one of the leading Urban Co-operative Banks, having branches in various places in Maharashtra, Gujarat and Karnataka, invites applications from young and dynamic Indian citizens for the post of 'Clerk'. Please note that Said vacancies are transferable to any location/office of the Bank. Total Number of ...
Home » ABHYUDAYA CO-OPERATIVE Bank Recruitment
ABHYUDAYA CO-OPERATIVE Bank Recruitment
ABHYUDAYA CO-OPERATIVE Bank Recruitment 2012 For The Post of Management Trainee
ABHYUDAYA CO-OPERATIVE Bank, the leading Urban Co-op. Bank in the country having a network of 105 branches spread across Maharashtra, Gujarat and Karnataka State. ABHYUDAYA CO-OPERATIVE Bank is looking for young and dynamic candidates who fulfill the following eligibility norms to work as Management Trainees in the Credit Dept. / Treasury Dept. ...
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subset: commoncrawl


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HONOLULU (AP) - Its frisky four strings are the sound of Elvis's "Blue Hawaii," of Tiny Tim tiptoeing through the tulips and lately, beyond all reason, of a popular "Bohemian Rhapsody" cover.
BOWLING GREEN, Ky. (AP) - It was a sight to make a classic car lover weep: A gaping sinkhole opened beneath the National Corvette Museum in Kentucky and swallowed eight prized cars like they were toys, piling them in a heap amid loose dirt and concrete fragments.
There may be a link between weather and the risk of suffering a stroke, say researchers who analyzed climate trends and hospital records on millions of Americans.
TORONTO (AP) - A Canadian study that many experts say has major flaws has revived debate about the value of mammograms. The research suggests that these screening X-rays do not lower the risk of dying of breast cancer while finding many tumors that do not need treatment.
OLYMPIA, Wash. (AP) - Gov. Jay Inslee said Tuesday he was suspending the use of the death penalty in Washington state for as long as he's in office, announcing a move that he hopes will enable officials to "join a growing national conversation about capital punishment."
RENO, Nev. (AP) - Drought worries are far from over, but the weekend storm in the Sierra more than doubled the mountain snowpack and should ensure normal river flows into western Nevada for at least part of the summer, federal water officials say.
HOUSTON (AP) - Two teenage boys were hoping to make a deal with the devil when they sexually assaulted and killed a 15-year-old suburban Houston girl in a satanic ritual, a prosecutor said Tuesday.
PITTSBURGH (AP) - A woman accused of hiding heroin in Happy Meals and selling them from a Pittsburgh drive-thru has been "emotionally crushed" by the allegations, her defense attorney said Tuesday, though he stopped short of denying the charges.
LEBANON, Tenn. (AP) - Investigators said Tuesday that a package sent to a rural Tennessee home exploded, killing a lawyer who lived there and injuring a woman.
MIAMI (AP) - Florida Highway Patrol Trooper Donna Jane Watts was on routine patrol early one morning when a Miami police car whizzed past at speeds that would eventually top 120 mph. Even with her blue lights flashing and siren blaring, it took Watts more than seven minutes to pull the speeder over.
CHEVY CHASE, Md. (AP) - Change is coming quickly to the Boy Scouts of America after years of turmoil and debate over its membership policy, with an openly gay 17-year-old in Maryland achieving the highest rank of Eagle Scout.
JACKSONVILLE, Fla. (AP) - The Florida man charged with fatally shooting a 17-year-old boy after an argument over loud music testified Tuesday that he thought he saw the barrel of a gun from the teen's SUV and that he feared for his life before firing his weapon.
MIAMI (AP) - A majority of Americans and even higher proportion of Floridians support re-establishing relations with Cuba, Washington's Cold War-era foe that remains blocked behind a five-decade economic embargo, results from a poll released Tuesday show.
JACKSON, Miss. (AP) - The Southern Poverty Law Center is calling on the U.S. government to reform cultural exchange programs, saying those have left some foreign participants vulnerable to exploitation and abuse.
McLEAN, Va. (AP) - The IRS on Tuesday lost a federal appeal in a legal battle over its effort to institute competency exams and other new regulations for as many as 700,000 paid tax preparers.
NEW YORK (AP) - Millions of fliers might soon want to buy new carry-on suitcases.
NEW YORK (AP) - New York could become the first U.S. city. to require warning labels on high-salt dishes at chain restaurants, taking campaigns to cut down on salt into new territory, health officials told The Associated Press on Tuesday.
GRADUATION ROBES GENDER-NEUTRAL IN MARYLAND SCHOOL DISTRICT: ROCKVILLE, Md. (AP) - Out of respect for transgender students, three high schools in Maryland's Montgomery County have begun using a single color for graduation robes to make them gender neutral.
DANNEMORA, N.Y. (AP) - Two murderers who used power tools to escape from prison must have taken days to cut through steel walls and pipes and break through the bricks, Gov. Andrew Cuomo said Sunday as a $100,000 reward was posted for information leading to their capture.
COLUMBUS, Ohio (AP) - The wide Ohio River is what ended the flight of a teenage couple authorities believe engaged in a crime spree that crossed into three states.
PHOENIX (AP) - Gripped by a prolonged drought, Arizona faces possible cuts to its main water supply in the next 18 months.
WASHINGTON (AP) - Fewer public college presidents hit the $1 million mark in earnings in 2014 compared with the previous year, according to a new survey.
SACRAMENTO (AP) - Tracey Clark's two teenage sons landed in intensive care, enveloped in gauze and their faces raw and red from burns over 40 to 60 percent of their bodies suffered in a fire, which prosecutors say was caused by an illegal hash-oil lab at their uncle's duplex.
LOUISVILLE, Ky. (AP) - Dr. David Jones is still impressed by the sight of it: A smiling fast-food worker taking the time to feed a disabled woman her favorite meal, a steak burrito.
WASHINGTON (AP) - A Montana woman says her brother was sexually abused by former House Speaker Dennis Hastert during the years when the GOP leader was a wrestling coach at a suburban Chicago high school.
LOS ANGELES (AP) - Jurors on Friday convicted a female Los Angeles police officer of felony assault for repeatedly kicking a handcuffed woman who later died.
AUSTIN, Texas (AP) - Before adjourning the 2015 legislative session, Texas became the first state in the country to name a "Tweeter Laureate." It's not a star quarterback or a pop star, but a state Supreme Court justice.
MOUNTAIN VIEW (AP) - Google is disclosing more details about the 12 accidents involving its self-driving cars so far as part of a commitment to provide monthly updates about the safety and performance of the vehicles.
ORO VALLEY, Ariz. (AP) - The condition of an 84-year-old Oro Valley man who was hospitalized after he was stung more than 2,000 times by bees is improving.
NEW YORK (AP) - Graydon Carter knew Caitlyn Jenner's cover would be popular, but this popular?
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Local conditions, severe-weather alerts, radar, and forecasts on your desktop.
Bing Weather is well worth the free download for its pretty, dead-simple design and comprehensive weather reports.
With an elegant interface, weather information, and interactive maps, Yahoo Weather is a must-have for weather watchers everywhere.
This system works well, but the appeal might be too limited to justify the price.
At the edge of our solar system, the spacecraft put itself into safe mode, leaving it temporarily unable to gather groundbreaking new data on the famous former planet.
Hey Siri, set my Ecobee to 72. The new HomeKit-enabled Ecobee3 smart thermostat responds to your voice commands and can detect the temperature in multiple rooms.
Accurate forecasts, beautiful animations and plenty of snark.
Have burning questions about Microsoft's upcoming operating system? Here are some answers.
Swirling cloud vortexes and billows of dust take on an otherworldly appearance when seen by astronauts and satellites looking down from orbit.
The world's largest social network plans to allow app makers to send photos, music and other stuff through its communication service.
Browse our list of cameras to see if do-it-yourself home security is right for you.


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armed robbery
Man Charged With Fatal Halloween Shooting, Robbery
Deshawn Johnson, 26, faces counts of first-degree murder, attempted murder and armed robbery for the attack that happened about 7:10 p.m. on Oct. 31, 2014, according to Chicago Police.
Cell Phone Store Employees Detain Gunman After Armed Robbery
Surveillance video shows one of the armed robbers aiming a handgun, maybe with a silencer attached, at a cell phone store employee, as another thief empties the cash drawer. CBS 2's Pamela Jones reports.
Robber Armed With Knife Targeting Lake View Restaurants
A man armed with a knife has robbed two Lake View fast-food restaurants in the last week on the North Side.
Man Charged With Numerous Armed Robberies On South Side
Officers linked the man to several armed robberies after he was arrested Friday night during the course of a robbery at a restaurant in the 6400 block of West 63rd Street, police said.
Prosecutors: Man Beat, Hacked Mother To Death With Knife
Dwight Brown, 40, was charged with one count of first-degree murder and one count of armed robbery, police announced late Tuesday.
Trio Charged With Slew Of Armed Robberies In Aurora
Martell White, 25, of the 15000 block of Madison Avenue in Dolton; Charles Campbell, 27, of the 1500 block of North Lorel Avenue; and Derrick Glasper, 27, of the 100 block of North 23rd Avenue in Bellwood, were each charged with three counts of armed robbery Tuesday, according to a statement from Aurora police.
Police Seek Help Identifying Suspect In NW Suburban Gas Station Robbery
Police are asking for the public's help to identify a suspect in an armed robbery of a gas station in unincorporated Palatine early Monday morning.
Man Free On Bond For Robbery Charged With Stealing Woman's Purse
A man free on bond after being charged with robbing an elderly man in west suburban Riverside in August was arrested last weekend and charged with another robbery in Chicago.
Security Guard Shot In Robbery At Bridgeport Diner
Shortly after 3 a.m., two masked men walked into Kevin's Hamburger Heaven, a 24-hour diner at the corner of Pershing Road and Wallace Street, and announced a robbery.
Pizza Delivery Driver Dies A Day After Shooting
Shot in the head during a robbery attempt early Monday, a pizza delivery driver has died.
Pizza Delivery Driver Seriously Wounded In Robbery, Shooting
Police were searching for the gunman who shot a pizza delivery driver in the head during a robbery attempt on the Northwest Side early Monday.
Second Man Charged With Armed Robbery On Orange Line
Robert Weaver, 47, of the 5000 block of South May Street faces three felony counts of armed robbery with a firearm in connection with the July 16 robbery, according to Chicago Police.
Man Charged In Downtown Convenience Store Robberies
Tydeon Woodland, 21, was charged with two counts of armed robbery. Police, who announced the charges late Wednesday, allege that Woodland robbed a convenience store in the 500 block of West Lake on Oct. 17 and another in the 100 block of South Clark on Oct. 23.
No Bail For Pair Charged With Shooting Off-Duty Police Officer
Cook County Judge Maria Kuriakos Ciesil told Jordan Bailey and Abdourahmane Soumare, both 19, that they were a "danger to themselves and society."
One Dead, Two Injured After Robbery Attempt, Police-Involved Shooting
Shortly before midnight, police officers saw two armed men approach two other men walking down an alley near the 7900 block of South Justine Street, police said. The suspects announced a robbery, and when they spotted police, the suspects shot the two men in the alley.
Armed Suspect Robs Orland Park Bank Branch
A gunman robbed a southwest suburban First Midwest Bank branch Monday afternoon, firing two shots inside the bank but wounding no one, authorities said.
Police: Man Robs Radioshack In Griffith, Ind.
Three men robbed a Radio Shack store at gunpoint Tuesday night in the Griffith Park Plaza, on Ridge Road in Griffith, Ind.
Cabbie Stabbed In Englewood Robbery
The driver, a 33-year-old man, was flagged down by a man in his 20s in the 5500 block of South Peoria Street about 12:05 a.m., police said. When the driver stopped, the man reached into the taxi, grabbed the driver's cell phone and stabbed him in the arm.
Man With Concealed Carry Permit Fires At Robber As Police Arrive
A man with a concealed carry permit got involved when he witnessed an armed robbery at a wireless store in southwest suburban Crestwood over the weekend.
Older Men With Guns Rob Pharmacy, Make Off With Viagra, Other Drugs
Causing little attention, two men in their late-50s entered a West Side medical center on the pretense of wanting to see the dentist. CBS 2's Dorothy Tucker reports.


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Singapore Prof Sentenced to Jail for Having Sex With Student
June 6, 2013
A former associate professor of law at the National University of Singapore was sentenced to five months of prison for having sex with a student and accepting gifts from her, Bloomberg reported. The judge imposed a longer jail sentence than that which was sought by prosecutors, stating that "corruption must be stamped out effectively and swiftly." The professor, Tey Tsun Hang, is accused of seeking expensive gifts and abusing his position of authority over the student. Tey maintains that the relationship was consensual. His lawyer has indicated plans to appeal.
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- Yale program to shift sexual assault culture goes beyond rape prevention
- Quick Takes: Tougher Oversight of NY For-Profits, Fault Line Could Force Campus to Move, $4B Drive for Cornell, Hibbing Athletes Charged in Rape, Convict Loses Admissions Suit, Fulbright Scholars Issue Reports, IRS Ruling for Stanford, Open U. Opens Wider
- Quick Takes: Colorado Keeps Affirmative Action, Social Scientist Set on Fire in Afghanistan, Racist Anti-Obama Graffiti, President for President-Elect, $300M for Chicago, Legal Move Against Animal Rights Extremist, Lack of Diversity in Sports, York Strike
- Is Academic Corruption on the Rise?
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In This Section
Journal Forum
Clean Audio for TV broadcast: An Object-Based Approach for Hearing-Impaired Viewers - April 2015
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AES Engineering Briefs Forum
Spooky Sounds: Interactive Audio Systems and Design for a Themed Attraction in an Academic Environment
The high-tech, interactive Gravesend Inn haunted hotel attraction features a large, distributed, audience-triggered sound system to implement a design both startling and evocative. Sound Designer Bruce Ellman and Systems Engineer John Huntington will discuss the challenges faced in developing this system and using it to teach Entertainment Technology Students.
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2002 Volkswagen Beetle Q&A
2002 Volkswagen Beetle Question: how do you open the trunk manually?
The devise inside the car does not open the rear lid and I would like to use my trunk for graceries, etc. I've read that it could be a cable, etec. and I really don't want to fix the stupid thing or have to take it in to a dealer (stealer). Can I just by pass all that and open it manually??:"? - rodne3
2 Answers
Answer 1
Are there instructions in your owners manual? Check here http://repairpal.com/automobile-owners-manuals-online or try this link you may be able to down load a free copy of the owner's manual for your vehicle http://www.autousermanual.com/ - patrick mannion
Answer 2
Unfortunately, mine is the same way, it will click, but will not pop open. It seems you will need two people, one to open the latch and the other to lift when you pull the cable or hit the button (04 - Beetle). Looks like the problem is with the plastic latch getting caught on the rubber flap. I will be applying some grease on mine to see if that helps. - zippy12
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text:
Discover the Dinosaurs
Discover the Dinosaurs is coming back to the Oakley Lindsay Center.
Discover the Dinosaurs is coming back to the Oakley Lindsay Center.
Rhet Reed and Molly Broughton Named 2015-2016 Tom and Becky.
Looking for a job? Browse local listings in the Townsquare Media online job fair!
Is a ghost haunting the Garden House Bed & Breakfast in Hannibal?
How would you like a 5-night stay in Mexico?
On July 4, the official 2015/2016 Tom and Becky were named for the City of Hannibal. Rhet Reed and Molly Broughton will serve as the city's ambassadors for the next year.
If you have been driving down Maine or 24th Streets in Quincy, you can't help seeing all the American flags in the yards. It happens every year around the 4th of July. American flags are placed on properties along several Quincy city streets. If you were curious as to who was responsible, here is your answer.
Pia Mia tells us about the making of her summer hit "Do It Again," as well as her personal favorite Song Of Summer '15 — Fetty Wap's "Trap Queen."
Independence Day has come and gone, but there's no reason to stop the celebrating.
Hardcore Jackie and Kelso 'shippers, rejoice: The former That '70s Show co-stars have said "I do."
No decisions have been made as to when the new season will begin.
An ATV accident eight miles north of Perry at 11:50 Sunday morning leaves a Quincy man with serious injuries.
An initial court appearance is set today (MON) for a young Quincy man accused of first degree murder in a double shooting.
The U.S. Department of Veterans Affairs is holding an outreach event tomorrow night in Shelbina, Missouri.
Discounted gate admission and carnival ride wristband tickets are now available for the 2015 Missouri State Fair at Missouri Break Time Convenience Stores, Orscheln Farm and Home Stores and Walgreens.


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38 year old man | Hollywood, FL, USA | Seeking women 26-41 within 50 miles
Want to be my Valentine next year?
Very outgoing guy with a warm personality, loyal and caring. I love what i do for a living, I see it more like a hobby although sometimes you have to stop me if not I'll be drawing in a napkin at a bar lol. I'm grateful for the family and friends that I'm surrounded by, its a blessing. That person I'm looking for needs to have a caring side, somebody that likes to explore new places, that is friendly. I like when a woman has a goofy attitude since I'm always smiling and or laughing. I'm happy with my social life always hanging out with good people. I'm willing to take things slow and open to a long term relationship with of course the right person These are just a few things about me so you have an idea but I'd like to tell you more in person so we have something to talk about in our date :O). Talk to you soon...
Camping , Coffee and conversation , Cooking , Dining out , Fishing/Hunting , Gardening/Landscaping , Hobbies and crafts , Movies/Videos , Museums and art , Music and concerts , Exploring new areas , Nightclubs/Dancing , Performing arts , Playing cards , Playing sports , Travel/Sightseeing , Video games , Volunteering , Watching sports , Wine tasting
Baseball, Basketball, Billiards / Pool, Bowling, Cycling, Dancing, Football, Golf, Inline skating, Martial arts, Other types of exercise, Swimming, Tennis / Racquet sports, VolleyBall, Walking / Hiking
I exercise 3-4 times per week.
I like Dogs, Fish, Horses
Pets require time and attention but I cannot offer neither right now...
Middle of the Road
Beaches, rivers, Spain, Puerto Rico, Virgin Islands, Saint Agustine,FL, Downtown Hollywood...you may find me almost every Saturday at Fort Lauderdale beach playing volleyball, bbqing or just hanging out with friends...
Favorites things includes bbqing, beach, volleyball tournaments, get together with friends, traveling, movies, design, be at the pool, road trips, random places and adventures...
Like to hang out with friends, play volleyball, cook, bbq's, go out, being outdoors, beach, house parties and get togethers, movies, bowling, mini-golf, board games, dominoes...
Elements of Style, The Wood Book, Chinesse Domestic Furniture
Z{{Cta}} {{#if HasMoreInfo}} ?{{CtaSecondary}} {{/if}}
|What he is looking for
|5'8" (172cms)
|4'10" (147cms) to 5'8" (172cms)
|Body type:
|About average
|Slender, About average, Curvy, Athletic and toned, Full-figured, A few extra pounds
|Black, Blue, Brown, Grey, Green, Hazel
|Auburn / Red, Black, Light brown, Dark brown, Blonde, Salt and pepper, Dark blonde
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|Social Drinker
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|Architecture / Interior design
|Administrative / Secretarial, Artistic / Creative / Performance, Executive / Management, Financial / Accounting / Real Estate, Labor / Construction, Legal, Medical / Dental / Veterinary / Fitness, Political / Govt / Civil Service / Military, Retail / Food services, Retired, Sales / Marketing, Self-Employed / Entrepreneur, Student, Education / Teacher / Professor, Technical / Science / Computers / Engineering, Travel / Hospitality / Transportation, Other profession, Nonprofit / Volunteer / Activist, Law enforcement / Security / Military, Fashion / Model / Beauty, Architecture / Interior design
I work for a mexican company designing furniture and interiors. Hopefully will start next year working from home as an independent designer...I love what I do!
|$35,001 to $50,000
|Less Than $25,000, $25,001 to $35,000, $35,001 to $50,000, $50,001 to $75,000, $75,001 to $100,000, $100,001 to $150,000, $150,001+
|Never Married
|Never Married, Widow / Widower, Currently Separated, Divorced
|Have kids:
|Yes, and they sometimes live at home, No, Yes, and they live away from home, Yes, and they live at home
|Wants kids:
|Definitely, Someday, Not sure, Probably not, No
|Latino / Hispanic
|Latino / Hispanic, Middle Eastern, Native American, White / Caucasian, Other
I come from Puerto Rico, a place with plenty to share, we have a lot of culture and plenty of places to visit...want to go for a vacation?
|Christian / LDS
|No preference
|English, Spanish
|No preference
|Bachelors degree
|Some college, Associates degree, Bachelors degree, Graduate degree, PhD / Post Doctoral
First got a associate degree as a draftman in PR, then went to architecture school (2 years in PR and 2 years in Milwaukee,WI) and took some furniture/woodworking courses along the way in order to learn more.


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Sabahi (Washington, DC)
News about the Horn of Africa, sponsored by the United States Africa Command, the military command responsible for supporting U.S. efforts in the region.
July 28, 2013
Somalia: Mogadishu Military Court Executes Four Soldiers for Murder
Four soldiers from the Somali National Army were executed Saturday (July 27th) after a military court in Mogadishu found them guilty of murder, Somalia's Garowe Online reported. Read more »
Kenya: Kenyan High Court Rejects Refugee Relocation Plan
Kenya's High Court ruled Friday (July 26th) that government plans to relocate about 55,000 mostly Somali refugees from urban areas into camps violate refugees' dignity and rights... Read more »
Tanzania: Tanzania, Interpol Conduct Joint Security Sweep
Tanzanian police and Interpol arrested 61 suspects for various crimes during a three-day security sweep throughout the country, Tanzania's Daily News reported Saturday (July 27th). Read more »
Kenya: Govt Threatens to Withhold Striking Teachers' Pay
The Kenyan government said it will not pay July salaries to teachers who participated in the four-week strike co-ordinated by the Kenya National Union of Teachers (KNUT), Kenya's... Read more »
Kenya: Downed Plane Recovered in Kenya, Three Swiss Dead
Three Swiss nationals are confirmed dead after the wreckage of a missing charter plane was found Saturday (July 27th) in Kenya's Aberdare National Park, Kenya's Capital FM... Read more »
Kenya: Kilonzo Wins Kenyan Senate Seat in Peaceful Vote
Mutula Kilonzo Junior has been declared the winner of Makueni County's senatorial election following the confirmation of results from 914 polling streams, Kenya's Capital FM... Read more »
July 26, 2013
Somalia: Attackers Kill One, Injure Five in Mogadishu
At least five people, mostly women who were selling milk at a market in Mogadishu's Hodan District, were injured Thursday night (July 25th) when unknown attackers threw a hand... Read more »
Somalia: Seventy-Four Arrested in Beledweyne Security Sweep
Somali government security forces and African Union Mission in Somalia troops arrested 74 suspects in a security sweep in Beledweyne Thursday (July 25th) following the killing of a... Read more »
Somalia: Al-Shabaab Boasts About Ramadan Rampage
In a series of recent Twitter messages, al-Shabaab boasted about how its fighters carried out over 100 attacks during the first half of Ramadan, and vowed to increase the violence... Read more »
Somalia: Marginalised Clan Seeks Political Rights in Somaliland Region
The Gaboye clan in the Somaliland region is taking steps to achieve greater political rights after facing years of political, social and economic marginalisation through... Read more »
Kenya: Ethiopian Drug Lord Arrested in Eastleigh
Suspected Ethiopian drug lord Soloman Walde Haulu was arrested in Nairobi's Eastleigh neighbourhood Thursday (July 25th) for re-entering the country illegally after he was deported... Read more »
Kenya: Makueni County Residents Vote in Senate Race
Voters in Kenya's Makueni County went to the polls early Friday (July 26th) to elect a new senator in by-elections, Kenya's Capital FM reported. Read more »
Tanzania: Kikwete Honours Fallen Soldiers On Heroes' Day
Tanzanian President Jakaya Kikwete praised the Tanzania People's Defence Force (TPDF) during a Heroes Day commemoration Thursday (July 25th), Tanzania's Daily News reported. Read more »
Somalia: Somaliland Consultation Council Hails Opposition Parties' Alliance
The Somaliland region's Council of Consultation and National Guidance Thursday (July 25th) praised an agreement reached between the two official opposition parties to form a united... Read more »
Kenya: Kenyan Police Kill Four Suspects in Petrol Station Shoot-Out
Kenyan police shot dead four suspected criminals at a petrol station in Nairobi's Ngara area Thursday (July 25th), while fifth suspect fled from the scene, Kenya's Daily Nation... Read more »
July 25, 2013
Somalia: UN Monitoring Group Mandate Extended for Somalia, Eritrea
The United Nations Security Council passed a 16-month extension of the mandate for the UN Monitoring Group on Eritrea and Somalia Wednesday (July 24th), the UN News Centre... Read more »
Kenya: World Bank Loans Kenya 21 Billion Shillings to Fight Poverty
The World Bank has loaned Kenya 21.7 billion shillings ($249 million) to support its poverty alleviation efforts, Kenya's Daily Nation reported Wednesday (July 24th). Read more »
Tanzania: Tanzanian Policeman Charged With Ivory Possession
A Tanzanian court has charged Field Force Unit Constable Ramadhani Selemani with possession of a 122-million shilling ($75,400) cache of ivory, Tanzania's Daily News reported... Read more »
Kenya: Parliament to Debate Amendments to Police Law
Kenya's parliament will review proposed amendments to the National Police Service Act that give the inspector general of police more powers and limit those of the National Police... Read more »
Kenya: Lack of Legal Framework Puts the Country's Natural Resource Ambitions At Risk
Kenya appears poised to reap billions of dollars from natural resources, but the absence of a proper legal framework could negate any of the country's future economic gains in... Read more »
Somalia: Clan Elders to Select Next Puntland Parliament
Puntland's regional parliament Wednesday (July 24th) voted unanimously to allow clan elders to select new members of parliament after the current legislature is dissolved in... Read more »
Somalia: Somali President Praises New Deal Plans
"Somalia has embraced the New Deal process", Somali President Hassan Sheikh Mohamud said Wednesday (July 24th) during his keynote address at the second New Deal core group meeting... Read more »
Somalia: Hargeisa Police Receive Emergency Response Vehicles
Somaliland regional Interior Minister Ali Mohamed Waranadde presented Hargeisa police on Tuesday (July 23rd) with 20 new vehicles that will be dedicated to responding to calls made... Read more »
Djibouti: Djibouti, China Discuss Energy Co-Operation
Djiboutian Minister of Energy in Charge of Natural Resources Ali Yacoub Mahamoud met with Chinese Ambassador to Djibouti Fu Huaqing Wednesday (July 24th) to discuss co-operation in... Read more »
Somalia: Puntland Appoints New Cabinet Officials
Puntland regional President Abdirahman Mohamed Farole appointed two new cabinet officials Wednesday (July 24th), UN-funded Radio Bar-Kulan reported. Read more »
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News & Updates
Law Articles, News, Promotions and Updates from Routledge and the Taylor & Francis Group.
Law Articles, News, Promotions and Updates from Routledge and the Taylor & Francis Group.
Routledge Law are delighted to announce plans for new research series, Law & Politics: Continental Perspectives. Read to find out more of what the series will be about and submit your book proposal.
Series edited by Andreas Philippopoulos-Mihalopoulos and Christian Borch.
Have you seen the newest research to join this new forward-thinking series yet? Discover Urban Commons, along with upcoming titles due later this year to recommend to your Librarian. Or why not see if your own research fits into this field of study and get in touch with an idea for a new book?
Have you had a chance to see the newest updates to 11th Edition of essential Contract Law textbook by Richard Stone and James Devenney yet? Click here now to find out more and to order your complimentary exam copy.
Discover the newest textbooks just published this year from April to June, request your complimentary exam copy or e-inspection copy, and make sure you have the most up to date edition of core reading for your course.
Congratulations to Michael Doherty, who was presented the Routledge/ALT Teaching Law with Technology Prize at the ALT Conference in Cardiff. The Prize recognises, rewards and champions innovation in teaching and learning, and is open to all law teachers in the UK. Read more about the winning project below.
Series edited by Denise Ferreira da Silva, Mark Harris and Brenna Bhandar.
This is a fresh new series with original research just added to the collection. Take a look to find out the scope of what this series will cover, recommend essential reading to your librarian so that it can be available for your institution and see what titles are available in paperback.
Be the first to find out what new updates have been made to upcoming 11th edition of essential textbook by Hilaire Barnett and pre-order complimentary exam copies for your course.
Frances Burton, author of Family Law textbook gives us the inside scoop on the new 2nd edition which has just published this year. Read our interview with her and find out more.
We've gathered together some of our key titles in Law and Religion, ahead of the Law and Religion Scholars Network conference in May. Even if you can't make it to Cardiff, you can still claim your 20% discount on all our featured titles, including the brand new Routledge Handbook of Law and Religion, and the Law and Religion series, edited by Norman Doe.


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We all crave to live with real wonder, in harmony with the Deeper Magic. Aren't you weary of a lesser magic? … a magic which deceives, drawing us into a death spiral.
It means that though the Witch knew the Deep Magic, there is a magic deeper still which she did not know. Her knowledge goes back only to the dawn of time. But if she could have looked a little further back, into the stillness and the darkness before Time dawned, she would have read there a different incantation. She would have known that when a willing victim who had committed no treachery was killed in a traitor's stead, the Table would crack and Death itself would start working backwards. (C.S. Lewis, The Lion, the Witch, and the Wardrobe)
Yes, there is a Deep Magic which has most things under its spell. The White Witch had a right to kill traitors to the true Kingdom. What the Witch doesn't know is that a deeper magic is written over all things.
It's this deeper magic that we want …


text:
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The Warp Wave boys broke out the Instagram filters for their first official edit! Just kidding guys, they shot it on VHS. It's retro.
admin one of the founders of the internet.
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Hey so Gakuen Heaven was really good thanks for telling me about it.
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Property is in very high demand and likely to sell quickly, even if it is overpriced or not in the best condition. Sellers receive multiple offers and the price is usually bid up above the seller's initial asking price.
Rent prices are relatively stable, and availability is good. If your yearly income is around $60,000, you can afford to rent in this market. Rent prices have not changed over the past 3 months. This is same as the state average of $1,218 and 98% lower than the country average of $2,388.
Trend data coming soon.
|For Sale: 217
|New: 31
|Recently Sold: 539
|Reduced: 52
|Average Home Price
|Average Sold Price
|Property Records: 14,174
|Foreclosed: N/A
The average home price in 28205 is $243,849, which is 8.7% higher than the average sold price in 28205 ($224,354) . The average home price per square foot in 28205 is $154 and about 4% of all homes in 28205 sold in the last 6 months. For 28205 home values, real estate prices, and city market trends, research the 14,174 property records or search our 539 recently sold or 217 homes for sale listings. The listings and properties in 28205 are only a part of the 3,391,244 properties and 84,511 homes for sale in North Carolina. Because of this, the average home price and average home value of 28205 also influence the average home price $202,624 and average sale price $222,872 of North Carolina. Listing counts, 28205 home prices and home values in 28205 are sourced daily from listing and property data on realtor.com®, which is the most up-to-date and accurate aggregation of real estate listings in the industry and includes approximately 800 regional MLSs and is the official website of the National Association of Realtors®.
|Median Age
|Median Household Income


text:
What's so good?
By David Peter Simon | Apr 26, 2013 | Total plays: 3,761
I'm really digging the trapstyle, with a touch of dark hip-hop, chopped up vocals, and synths that snake across claps that seemingly last for days. Luckily for you, this song is available for free download. I've been blasting it on repeat for the last hour and am already in trouble with a few coworkers seated nearby.
We look forward to checking out his Soulection debut later this year. Check out more trap goodness with tracks like "Hypergloss."
Sounds like: Flying Lotus, Bahwee, Sweater Beats


text:
subdudes home
the subdudes, music, band, rock and roll, Tommy Malone, John Magnie, Steve Amedee, Tim Cook, Johnny Ray Allen, zydeco, New Orleans, louisiana, accordion, tambourine, all the time in the world, sarita, papa dukie, one time, carved in stone,
2015 Tour dates
Check the "Concerts" page for more info
or select one of the venues below for ticket info
July 15th Moe's Alley. Santa Cruz, CA
July 16th Freight and Salvage. Berkeley, CA
July 18th Navarro General Store. Navarro, CA
July 19th Rancho Nicasio Bar & Restaurant. Rancho Nicasio, CA
Sept 12th Sisters Folk Festival. Sisters, OR
Oct 14th Rams Head Onstage. Annapolis, MD
Oct 15th The Birchmere. Alexandria, VA
Oct 16th The Sellersville Theatre. Sellersville, PA
Oct 17th Swyer Theatre at The Egg. Albany, NY
Contact the subdudes Management
The Roots Agency
177 Woodland Avenue
Westwood, NJ 07675 USA
Tel: 201-263-9200
Fax: 201-358-8784


text:
No problems with FF3.6.6 Rated 5 out of 5 stars
I've been using Morning Coffee for quite a while and with FF3.6.6 since it became available. MC works flawlessly every time I use it and I have a lot of stuff input for every day. Don't know why people are having problems but they must have something else going on with their systems other than FF3.6.6This review is for a previous version of the add-on (1.33).


text:
Michelle Obama wore a floral-print dress with ruffle-lace detailing to a luau on the White House lawn yesterday. Mrs. O suspects this is a Tracy Feith creation. She accessorized with the requisite lei. Bo Obama went naked. See the full look (and Bo!) in the Michelle Obama Look Book.
See it »


text:
SparkFun Electronics will be closed on July 3rd, 2015 in observance of Independence Day. Any orders placed after 2:00pm MT on July 2nd will be shipped out after the weekend. Thanks!
This product has been retired from our catalog and is no longer for sale. This page is made available for those looking for datasheets and the simply curious.
Description: Replacement: None. We do not have a direct replacement for this relay. We may have other relays that could be similar though. This page is for reference only.
This is a high quality single pole, double throw (SPDT) sealed relay from Omron. Use them to switch high voltage, and/or high current devices. The coil voltage on this relay is rated at 12VDC, and the load current is rated up to 10A.
Is it 10A@125VAC as stated in features or 10A@250VAC as shown in the picture?
No reviews yet.


text:
Mona Vale Surf Cam & Surf Report
Feature Film: My Eye's Won't Dry 3
@ 10 sec
15 min ago
L 7:13 AM (0.4m)
H 1:31 PM (1.5m)
L 7:30 PM (0.6m)
H 1:39 AM (1.6m)
Regional Surf Report[?]
Surf Report Info
Region: Palm Beach to Manly - Fairy Bower
Reporters location:
Coastalwatch surf reporters are the saltiest locals around. Part fish, part shark, part human, they live for the waves and are usually more local than the locals. They'll be up before dawn waiting for first light to reveal the days surf conditions and can sense a change of wind from a sparrows fart. Each reporter covers a region of coastline which includes many number of surf spots and beaches. Please consider there may be possible variations between this report and your local spot due to differences in orientation to the coast and any local idiosyncrasies that may also effect the swell and weather patterns.
by Captain
8/07/2015 7:07 AM | Report
Today's rating - Pretty Good
Morning Report: Waves 2-4ft,Swell SSE @10 secs,Winds WSW-S-SSE 10-15 knots. Bit of a lumpy south swell with size ranging 2-4ft and early offshore's returning a bit of form. S facing biggest and doesn't look too bad some beaches. Into the day expecting a touch more energy as moderate winds tend south. Plenty breaking, nothing epic with probably enough swell for cleaner protected ends as winds shift. ...Check out the Coastalwatch Plus Standout Sessions contest & win a trip to the Maldives.
Today's Outlook
Swell: 1.6m
Wind: WSW 10-20 kts
Best at: South-facing beaches
Conditions: Semi-clean
Swell: 1.9m
Wind: SSE 10-20 kts
Best at: Protected beaches
Conditions: Semi-clean
Sponsor recommended
The best board for today is :
The best wetsuit for today is :
Tomorrow's Surf Forecast
@ 10 sec
Marine Outlook
Winds: South to southeasterly 10 to 15 knots, reaching up to 20 knots offshore in the morning.
Seas: 1 to 1.5 metres, decreasing to 1 metre around midday.
Swell: Southerly 1.5 metres, increasing to 1.5 to 2 metres offshore. Weather: Partly cloudy. 50% chance of showers this morning.
Mona Bowls
by WildmanFilms
01 Jun 2015
507 views
To late
by WildmanFilms
01 Jun 2015
331 views
by Ticka
26 May 2015
215 views
G&T mona
by lulu16
01 Mar 2015
129 views
Not yet rated.
Mona Vale Early
by MW100
01 Mar 2015
97 views
Not yet rated.
Mona Vale Pot of Gold
21 Aug 2014
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20 Aug 2014
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Ocean cruiser.
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225 views
Move it
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23 Apr 2014
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My favourite place to be
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23 Apr 2014
323 views
Forecaster Blog: Impending East Coast Low Threatens Storm-Swell For The NSW Coast
East Coast Lows can have seriously good implications for surfing conditions across the Eastern Seaboard.
Bali, Indonesia Surf Forecast 8 - 20 July 2015
Feature Film Of The Month: My Eye's Won't Dry 3
Professional Surfer and Point of View cinematography master, Brian Conley presents the 3rd edition to his My Eyes Won't Dry surf film series.
Video: Get Frothed Out On J-Bay With Jay Davies and Ricardo Christie
"Thinkin' Terry, Curren" (said with a Kiwi accent).
Sanbah Surf
Sanbah Surf Shop. We surf, we skate, we share what we know.
Rusty Manly
Rusty is honoured to announce its first flagship store located in the iconic surf town of Manly.
DMS Surfboards
At DMS the vision has always been to create premium-handcrafted surfboards using the best materials, superior craftsmanship and functionality that is second to none.
Zink Surf
Zink Surf is the established store on the coast when it comes to boards and hardware.
Dripping Wet Manly
Check out Dripping Wet Manly and let their qualified staff help you get the most out of your next surfboard.
Sequence: Surfer Spreads Mate's Ashes In The Swell of The Decade, Mid-Tube
Wave of The Week: Surfing mateship is a beautiful thing.
The Largest Waves Ever Surfed In Australia (Maybe!), Waterski Barrels & A Super Gnar Surf Tattoo – This Week In Surfing
Ten Things From Surfing and The Internet On The Week That Was July 3, 2015
Video: Great White Shark Eating Whale Near Coffs Harbour NSW
Shark feeding frenzy on the NSW North Coast
Second Shark Incident In Two Days On North Coast NSW
Surfer bumped off board at Lennox Head, Skullcandy Oz Grom Open Suspended


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Rounding and estimation
Scientific calculators are a wonderful invention, but they're only as good as the...
Scientific calculators are a wonderful invention, but they're only as good as the people who use them. If you often get an unexpected – or ridiculous – result when you press the 'enter' button, this unit is for you. Learn how to do a calculation correctly and get the right answer every time.
By the end of this unit you should be able to:
- round a given whole number to the nearest 10, 100, 1000 and so on;
- round a decimal number to a given number of decimal places or significant figures;
- use rounded numbers to find rough estimates for calculations;
- use a calculator for decimal calculations involving +, −, × and ÷, giving your answer to a specified accuracy (e.g. decimal places or significant figures) and checking your answer by finding a rough estimate;
- check your answers to calculations by ensuring that the correct calculation has been done, in the correct order;
- check your answers by checking that the units are consistent;
- check your answers by checking the result against a rough estimate;
- check your answers by checking that the answer makes sense in the context of the problem.
- Duration 5 hours
- Updated Friday 10th June 2011
- Introductory level
- Posted under Mathematics Education
- Current section: Introduction
- Learning outcomes
- 1 Rounding
- 1.1 Rounding in daily life
- 1.2 Rounding whole numbers
- 1.3 Rounding in general
- 1.4 Rounding decimals
- 1.5 Significant figures
- 1.6 Significant figures for numbers less than one
- 2 Estimation
- 3 Checking your answers
- 3.1 Have I done the right calculation?
- 3.2 Have I used the correct order for my calculation?
- 3.3 Have I given due consideration to units of measurement?
- 3.4 Did I make a rough estimate to act as a check?
- 3.5 Does the answer make sense in the real world?
- 3.6 Additional practice
- 4 OpenMark quiz
- Acknowledgements
Study this free course
Enrol to access the full course, get recognition for the skills you learn, track your progress and on completion gain a statement of participation to demonstrate your learning to others. Make your learning visible!
Rounding and estimation
For many calculations you use a calculator. The main aim of this unit is to help you to do this in a sensible and fruitful way. Using a calculation to solve a problem involves four main stages:
Stage 1: working out what calculation you want to do;
Stage 2: working out roughly what size of answer to expect from your calculation;
Stage 3: carrying out the calculation;
Stage 4: interpreting the answer – Does it agree with the rough estimate? Does it make sense in terms of the original problem?
This unit focuses on Stages 2 and 4.
This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offer in this subject area [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .
Archive content
This is an extract from an Open University course which is no longer available to new students. If you found this interesting you could explore more free Mathematics Education courses or view the range of currently available OU Mathematics Education courses.
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Publication details
Originally published: Friday, 10th June 2011
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