Decoders:

n to m decoder is the combinational circuit which convert binary information from n lines of input to m lines of output and m=<2 n. Let’s have an example of 3 to 8 decoder. This encoder just puts the 1 on the line which is equal to the decimal equivalent of binary number abc2 at the input and 0 on the remaining lines. There is an ENABLE input which when 0 activates the decoder circuit otherwise decoder is deactivated and it does not matter what we have at the inputs any more. The following table shows the functioning of decoder:

a              b             c              D0           D1          D2           D3           D4          D5           D6          D7

0              0             0              1              0              0              0             0             0              0             0

0              0             1              0              1              0             0             0              0              0              0

0              1             0             0              0              1              0              0              0              0              0

0              1              1              0              0              0              1             0             0             0             0

1              0              0              0              0              0              0              1              0             0              0

1              0              1              0              0              0              0              0              1             0              0

1              1              0              0              0              0              0             0              0              1              0

1              1              1              0              0              0             0             0              0             0              1

As we see that D0 is 1 only for a=0 b=0 c=0 hence we can directly write equation as D0=a’b’c’=m0

Similarly we have D1=a’b’c= m1, D2=a’bc’= m2, D3=a’bc= m3, D4=a’bc= m4, D5=ab’c= m5, D6=abc’= m6,

D7=abc= m7 and from the equations we can draw the digital circuit.
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