COMPUTER SCIENCE AND ENGINEERING
COMPUTER ARCHITECTURE
Question
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Simplified form of the boolean expression (X + Y + XY) (X + Z) is

X + Y + Z


XY + YZ


X + YZ


XZ + Y

Explanation:
Detailed explanation1: Y = Y. Hence, the reduced form of the Boolean expression A = XY + X(Y+Z) + Y(Y+Z) is A = Y+XZ.
Detailed explanation2: The Karnaugh map (K–map), introduced by Maurice Karnaughin in 1953, is a gridlike representation of a truth table which is used to simplify boolean algebra expressions. A Karnaugh map has zero and one entries at different positions.
Detailed explanation3: It is known that the product of two values can be established by the conjunction of x and y. And the sum of two values can be established by the disjunction of x and y. The result of the proposition is shown in the truth below. Hence, the value of the Boolean function xy + xz is 11100000.
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