Question

Construct a combinational circuit using 2-input basic gates which has 3 inputs A,B & C

and 3 outputs X,Y &Z. When the decimal equivalent of the binary input is 0, 1, 5 or 3,

the decimal equivalent of the binary output is one greater than the input and when

decimal equivalent of the binary input is 4,2,6 &7 , the decimal equivalent of binary

output is one less than the input.

Answer 1

Design procedure:

1. Derive the truth table that defines the required relationship between

inputs and outputs.

Obtain the simplified Boolean functions for each output as a function of the

input variables.

Map for output A:

The simplified expression from the map is:

$A =xz+xy+yz$

Map for output B:

The simplified expression from the map is:

$B = x'y'z +x'yz'+ xy'z'+ xyz$

Map for output C:

The simplified expression from the map is:

C =z'

Draw the logic diagram.

$A =xz+xy+yz\\ B = x'y'z +x'yz'+ xy'z'+ xyz\\ C=z'$