ITPEC FE Morning April 2021 Question 22
Which of the following is not an implementation of the function F = A•B + C•D? Here, “•” represents the logic AND operation, and “+” represents the logic OR operation in the expression.
Explanation
Circuit (c), two NANDs into a NOR — its output is A•B•C•D, a product of the two terms, not their sum.
In (b), (c) and (d) the first level is the same: two NAND gates give P = A•B and Q = C•D. Only the output gate differs.
- •(b) NAND: P•Q = P + Q = A•B + C•D by De Morgan's law
- •(d) OR with inverted inputs: P + Q = A•B + C•D, the same gate as a NAND, drawn another way
- •(c) NOR: P + Q = P•Q = A•B•C•D
Check (c) with A = B = 1, C = D = 0: F should be 1, but P = 0, Q = 1 and the NOR outputs 0.
Answer (c)
Why not others:
- •(a) — the direct form: two AND gates into an OR gate is A•B + C•D as written
- •(b) — NAND–NAND is the standard two-level form of a sum of products, equal to F by De Morgan's law
- •(d) — an OR gate with bubbles on its inputs is a NAND gate, so this is circuit (b) redrawn
Key rule: A NAND gate equals an OR gate with inverted inputs, so NAND–NAND implements any sum of products; changing the output gate to NOR turns the sum into a product.
Hardware · AI-written, may contain errors
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