ITPEC FE Morning October 2020 Question 22
ITPEC FE Morning October 2020 — Question 22 of 80
De Morgan's Law — NOT gates before OR create NAND — insert a gate before each OR input to build NAND.
NAND = ¬(X · Y)
By De Morgan's Law: ¬(X · Y) = ¬X + ¬Y
- •Place a NOT gate on each input of the OR gate
- •
OR(¬X, ¬Y) = ¬X + ¬Y = ¬(X · Y)= NAND
Why not others:
- (a) AND — single-input AND is identity; result is still X + Y (plain OR)
- (b) NOR — a 2-input gate applied to a single signal acts as NOT, but NOT is the more precise answer
- (d) OR — single-input OR is identity; result is still X + Y (plain OR)
Key rule: De Morgan: ¬(A · B) = ¬A + ¬B → NOT before OR = NAND; NOT before AND = NOR.
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