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

  1. A.

    xz + y'z

  2. B.

    xz' + zx'

  3. C.

    x'y + zx'

  4. D.

    None of these

Attempted by 40 students.

Show answer & explanation

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'.

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