In the Boolean expression f = (A + B + C) X Y, when will f be 1?

In the Boolean expression f = (A + B + C) X Y, when will f be 1?

• A. X = 0 or Y = 0
• B. All of A,B,C must be 1
• C. X = 1, Y = 1, and at least one of A, B, C is 1
• D. X = 1, Y = 0

Answer: (C)

The expression multiplies three conditions: the OR of A, B, and C, and the two inputs X and Y. For the whole thing to be 1, all three parts must be 1. The OR term (A + B + C) is 1 whenever any one of A, B, or C is 1, and it’s 0 only if all three are 0. So f will be 1 exactly when X is 1, Y is 1, and at least one of A, B, or C is 1. If none of A, B, C is 1, f is 0 no matter what X and Y are; if either X or Y is 0, f is 0 regardless of A, B, C.

The expression multiplies three conditions: the OR of A, B, and C, and the two inputs X and Y. For the whole thing to be 1, all three parts must be 1. The OR term (A + B + C) is 1 whenever any one of A, B, or C is 1, and it’s 0 only if all three are 0. So f will be 1 exactly when X is 1, Y is 1, and at least one of A, B, or C is 1. If none of A, B, C is 1, f is 0 no matter what X and Y are; if either X or Y is 0, f is 0 regardless of A, B, C.