Mathematical Foundation of Computer Science

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N-COM\APPENDIX.PM5

370 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE

wx

yz

or or

or

Fig. A.16

Example 5.7. Simplify the K-map shown in Fig. A.17.

wx

yz

wx′′

wx′

wx

w

wx′

yz′ yz′ yz

y

x

z

yz′

1

1

11

1

11

1

1

Fig. A.17

f(x, y, z) = w′ x′ + w′ xy + x y z + w z + y′ z′ (5 minterms)

Solution: Since, we know that maxterms is dual to the minterms; so in the K-map represen-
tation of any Boolean function if we groups the 0’s instead of 1’s we obtain the minimized
Boolean function that is in products of maxterms. In the previous example grouping of 0’s
instead 1’s are shown below in Fig. A.18.