ITPEC FE Morning April 2023 Question 20

Topic: Hardware

Which of the following is the logic circuit that is equivalent to the logical expression ABC + AC?

Explanation

An OR gate on A and B, feeding an AND gate with C — the expression simplifies to C(A + B).

  • •Factor out C: ABC + AC = C(AB + A)
  • •Absorption: AB + A = A + B; if A = 1 both sides are 1, and if A = 0 both equal B
  • •So the output is C(A + B), which is circuit (c)

Answer (c)

Why not others:

  • •(a) — inverts A + B and ORs in BC, giving AB + BC; at A = B = C = 0 it gives 1, but the expression gives 0
  • •(b) — computes A + ABC; at A = B = C = 0 it gives 1, but the expression gives 0
  • •(d) — computes AB + BC; at A = 1, B = 0, C = 1 it gives 0, but AC = 1

Key rule: Simplify the expression first (factor, then the absorption law AB + A = A + B) and match the smaller form; one input where a circuit disagrees is enough to reject it.

Hardware · AI-written, may contain errors

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