Consider the Boolean expression F = (X + Y + Z)(X′ + Y)(Y′ + Z). Which of the following Boolean expressions is/are equivalent to F′ (the complement of F)?
A. (X′ + Y′ + Z′)(X + Y′)(Y + Z′)
B. XY′ + Z′
C. (X + Z′)(Y′ + Z′)
D. XY′ + YZ′ + X′Y′Z′
Choose the correct answer from the options given below:
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Correct answer: B. B, C and D Only
Explanation
By De Morgan, F′ = X′Y′Z′ + XY′ + YZ′ (D). This simplifies to XY′ + Z′ (for Z = 0 it is always 1; for Z = 1 it reduces to XY′), which is B. (X + Z′)(Y′ + Z′) also expands to XY′ + Z′ (C). A gives 0 for X = Y = Z = 0, where F′ = 1.More Computer System Architecture questions
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