ITPEC FE Morning April 2020 Question 23
Which of the following is an appropriate equation of the XOR operator? Here, “ · ” represents the logical AND, “+” represents the logical OR, and P represents the inverse of P in the logical expression.
Explanation
(A + B) · NOT (A · B) — XOR is 1 when at least one input is 1 (the OR) but not both (the NAND).
Read the XOR condition as two parts joined by AND: at least one input is 1, which is A + B, and the two are not both 1, which is A · B. So X = (A + B) · (A · B).
The last column is 0, 1, 1, 0: exclusive OR.
Answer (b)
Why not others:
- •(a) — ANDs A · B with its own inverse, so it is always 0
- •(c) — A · B needs both inputs 1 while A + B needs both 0, so it is always 0
- •(d) — ANDs A + B with its own inverse, so it is always 0
Key rule: A term ANDed with its own complement is always 0; check a candidate expression against the four rows of the truth table.
Basic Theory · AI-written, may contain errors
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