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show the block diagram for a decoder, the truth table for which is shown below.

ID: 1921641 • Letter: S

Question

show the block diagram for a decoder, the truth table for which is shown below. the available components are one-, two-, and three-input NAND gates. (A one-input NAND is an inverter.

       Inputs                  Outputs

E1   E2   a   b              1   2   3

0      X    X   X             1   1   1

X     0     X   X             1   1   1

1      1    0    0              1   1   1

1      1    0    1              0   1   1

1      1     1   0              1   0   1

1      1    1    1              1   1   0

Explanation / Answer

the above truthtable illustrates the 2 to 4 decoder . Here the E1,E2 are the enable inputs. both should be high for the circuit to be active irrespective of the inputs a and b.This decoder has inverted outputs.For each combination of the values of the inputs exactly one of the output lines should be zero.When a binary coded decimal digit is used as a input to this decoder one of the output lines wil be low indicating which of the 4 decimal digits is present so the outputs are 1=E1E2NOTA B 2=E1E2A NOTB 3=E1E2AB