Which function does NOT implement the Karnaugh map given below?
2000
Which function does NOT implement the Karnaugh map given below?
- A.
(w + x)y
- B.
xy + yw
- C.
(w + x)(w' + y)(x' + y)
- D.
None of the above
Attempted by 28 students.
Show answer & explanation
Correct answer: D
Read the K-map using rows xy = 00, 01, 11, 10 and columns wz = 00, 01, 11, 10. The required 1-cells are the entire row xy = 11 and the two cells in row xy = 01 where w = 1. Therefore the function represented by the K-map is y(x + w).
Option A: (w + x)y = y(w + x), so it implements the map.
Option B: xy + yw = y(x + w), so it also implements the map.
Option C: (w + x)(w' + y)(x' + y). Since (w' + y)(x' + y) = y + w'x', this becomes (w + x)(y + w'x') = y(w + x). The second term is zero because (w + x)w'x' = 0. Hence option C also implements the same map.
Thus A, B, and C all implement the Karnaugh map. The function that does NOT implement it is none of them, so the correct option is D: None of the above.