Digital-Logic-Design
October 15, 2023K-Map
October 15, 2023Digital-Logic-Design
| Question 3 |
Consider the following Boolean expression.
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Question 3 Explanation:
XY’+Z’ is a minimal SoP expression which represents the function (X,Y,Z).
The expression XY’ + YZ’ + X’Y’Z’ can be reduced to XY’+Z’
XY’ + YZ’ + X’Y’Z
= Y’(X+X’Z’) + YZ
= Y’(X+Z’) + Y
= XY’ + Y’Z’ + YZ’
= XY’ + (Y’+Y)Z’
= XY’ + Z’.
The expression (X+Z’)(Y’+Z’) is a PoS expression which also represents the same function (X,Y,Z).
Correct Answer: C
Question 3 Explanation:
XY’+Z’ is a minimal SoP expression which represents the function (X,Y,Z).
The expression XY’ + YZ’ + X’Y’Z’ can be reduced to XY’+Z’
XY’ + YZ’ + X’Y’Z
= Y’(X+X’Z’) + YZ
= Y’(X+Z’) + Y
= XY’ + Y’Z’ + YZ’
= XY’ + (Y’+Y)Z’
= XY’ + Z’.
The expression (X+Z’)(Y’+Z’) is a PoS expression which also represents the same function (X,Y,Z).