Topic: Digital Logic
The given Boolean expression is:
$X^{\prime}Y^{\prime}Z^{\prime}+X^{\prime}YZ^{\prime}$
Which of the following represents the Karnaugh map for the above expression?
- A. Option showing 1s at X'Y'Z' and X'YZ' in a 4-row (X'Y', X'Y, XY, XY'), 2-column (Z', Z) format
- B. Option showing 1s at X'Y'Z and X'YZ in a 4-row format
- C. Option showing 1s in a 2-row format that do not match the expression
- D. Option showing 1s in a 2-row format that do not match the expression
Answer: A. Option showing 1s at X'Y'Z' and X'YZ' in a 4-row (X'Y', X'Y, XY, XY'), 2-column (Z', Z) format
Explanation: The given expression has two minterms: $X'Y'Z'$ and $X'YZ'$. In a Karnaugh map with rows representing XY combinations and columns representing Z combinations, we need 1s located precisely at the cell for $X'Y'$ row under $Z'$ column, and the cell for $X'Y$ row under $Z'$ column. Option (a) accurately reflects this placement.