Minimum sum-of-products expression for f(w, x, y, z) shown in the Karnaugh map…
2002
Minimum sum-of-products expression for f(w, x, y, z) shown in the Karnaugh map below is:
yz \ wx | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
00 | 0 | 1 | 1 | 0 |
01 | X | 0 | 0 | 1 |
11 | X | 0 | 0 | 1 |
10 | 0 | 1 | 1 | X |
- A.
xz + y'z
- B.
xz' + zx'
- C.
x'y + zx'
- D.
None of these
Attempted by 40 students.
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Correct answer: B
Read the K-map with rows yz = 00, 01, 11, 10 and columns wx = 00, 01, 11, 10.
The four 1s in rows yz = 00 and 10 with columns wx = 01 and 11 form a group where x = 1 and z = 0, giving the term xz'.
The 1s in rows yz = 01 and 11 with column wx = 10 can be grouped with the don't-care cells in column wx = 00. In that group x = 0 and z = 1, giving x'z, which is the same as zx'.
Therefore the minimum SOP is xz' + zx'.