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# Design a combinational circuit with four inputs (A, B, C and D) and four outputs (W, X, Y and Z). When the binary input is less than 10 the binary output is two greater than the input. When the binary input is equal or greater than 10 the binary output

Design a combinational circuit with four inputs (A, B, C and D) and four outputs (W, X, Y and Z). When the binary input is less than ten the binary output is two greater than the input. When the binary input is equal or greater than ten the binary output is three less than the input.

## Solutions

##### Expert Solution

Truth Table :

 A B C D W X Y Z 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0

Karnaugh map:

W:

 AB\CD 00 01 11 10 00 0 0 0 0 01 0 0 1 1 11 1 1 1 1 10 1 1 1 0

W= BC + AC' + AD

X:

 AB\CD 00 01 11 10 00 0 0 1 1 01 1 1 0 0 11 0 0 1 0 10 0 0 0 1

X= A'B'C + B'CD' + A'BC' + ABCD

Y:

 AB\CD 00 01 11 10 00 1 1 0 0 01 1 1 0 0 11 0 1 0 1 10 1 1 0 1

Y= A'C' + B'C' + C'D + ACD'

Z:

 AB\CD 00 01 11 10 00 0 1 1 0 01 0 1 1 0 11 1 0 0 1 10 0 1 0 1

Z= A'D + B'C'D + ACD' + ABD'

Combinational Circuit:

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