Question

Consider the Boolean function in a CPU control unit: \[ Y = (A + B . C') . (A . B + C) \] Which of the following is the correct simplified expression for \( Y \)?

• A. \( A . B + C \)
• B. \( A . C + A' . B + B . C' \)
• C. \( A . C + A' . B . C' \)
• D. \( A . C + A' . B . C' \)

Hint:

To simplify Boolean expressions, use distribution, combining like terms, and applying Boolean identities like \( A . A = A \) and \( A + A' = 1 \).

Answer 1

The Correct Option is C

We are given the Boolean function: \[ Y = (A + B . C') . (A . B + C) \] First, apply distribution to the given expression: \[ Y = A . (A . B + C) + B . C' . (A . B + C) \] Expanding each term: \[ Y = A . A . B + A . C + B . C' . A . B + B . C' . C \] \[ Y = A . B + A . C + B . C' . A . B + 0 \] Since \( B . C' . A . B = A . B \), we get: \[ Y = A . B + A . C \] Thus, the correct answer is option (C).