Which of the following is correct for f(x, y, z) =Σ(0, 2, 4, 5, 6) ?
2025
Which of the following is correct for f(x, y, z) =Σ(0, 2, 4, 5, 6) ?
Answer: B. f = xy' + z' — The Boolean function is defined by minterms 0, 2, 4, 5, and 6. Convert minterms to binary: 0 (000), 2 (010), 4 (100), 5 (101), 6 (110). Using a Karnaugh map,…
- A.
f = x'y + z
- B.
f = xy' + z'
- C.
f = xy' + z
- D.
f = x'y + z'
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Correct answer: B
The Boolean function is defined by minterms 0, 2, 4, 5, and 6.
Convert minterms to binary: 0 (000), 2 (010), 4 (100), 5 (101), 6 (110).
Using a Karnaugh map, minterms 0, 2, 4, and 6 form a group of four where z = 0. This simplifies to the term z'.
The remaining minterm 5 can be grouped with minterm 4. This pair corresponds to x = 1 and y = 0, simplifying to the term xy'.
Combining these results yields the simplified expression f = xy' + z'.