ITPEC FE Morning April 2022 Question 1
Topic: Basic Theory
For logical variables A and B, which of the following is equivalent to the NOR operation on A and B? Here, A + B, A · B, and A are OR, AND, and NOT operations on the corresponding variables, respectively.
Explanation
NOT A AND (A OR NOT B) — NOR is A · B by De Morgan's law, so simplify each option until one reduces to it.
- •NOR: A + B = A · B, which is 1 only when A = 0 and B = 0
- •Option (a): A · (A + B) = A · A + A · B
- •A · A = 0 (a variable and its complement), so the result is A · B, which is NOR
Answer (a)
Why not others:
- •(b) — absorption reduces A · (A + B) to A, which is also 1 for A = 0, B = 1
- •(c) — B · (A + B) = A · B, the AND operation, 1 only when both inputs are 1
- •(d) — absorption reduces B · (A + B) to B, which is also 1 for A = 1, B = 0
Key rule: Expand, then drop any term containing a variable ANDed with its own complement; X · (X + Y) = X removes the rest.
Basic Theory · AI-written, may contain errors
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