Four Boolean variables a, b, c, d are present in the Boolean equation as…
Four Boolean variables a, b, c, d are present in the Boolean equation as follows
abc’ + 1d + ac = 1b’c = 1
Which of the following can be the correct option for the equation?
Answer: A. a=1 b=0 c=1 d=0 — Method: evaluate the left expression a·b·c' + d + a·c and the right expression b'·c for each given assignment; the equation holds when both evaluate to 1. For…
- A.
a=1 b=0 c=1 d=0
- B.
a=1 b=1 c=0 d=0
- C.
a=0 b=0 c=1 d=0
- D.
a=0 b=0 c=0 d=1
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Correct answer: A
Method: evaluate the left expression a·b·c' + d + a·c and the right expression b'·c for each given assignment; the equation holds when both evaluate to 1.
For a=1, b=0, c=1, d=0: a·b·c' = 1·0·0 = 0, d = 0, a·c = 1·1 = 1, so left = 0 + 0 + 1 = 1. Right b'·c = 1·1 = 1. Both sides = 1, so this assignment satisfies the equation.
For a=1, b=1, c=0, d=0: a·b·c' = 1·1·1 = 1, d = 0, a·c = 1·0 = 0, so left = 1 + 0 + 0 = 1. Right b'·c = 0·0 = 0. Left ≠ right, so this assignment does not satisfy the equation.
For a=0, b=0, c=1, d=0: a·b·c' = 0·0·0 = 0, d = 0, a·c = 0·1 = 0, so left = 0. Right b'·c = 1·1 = 1. Left ≠ right, so this assignment does not satisfy the equation.
For a=0, b=0, c=0, d=1: a·b·c' = 0·0·1 = 0, d = 1, a·c = 0·0 = 0, so left = 1. Right b'·c = 1·0 = 0. Left ≠ right, so this assignment does not satisfy the equation.
Conclusion: the only assignment that makes both sides equal to 1 is a=1, b=0, c=1, d=0.