The Boolean expression Y(A, B, C) = A + BC is to be realized using 2-input…
The Boolean expression Y(A, B, C) = A + BC is to be realized using 2-input NAND Gates only. The minimum number of NAND gate required for this realization is____________.
Answer: 3 — Key idea: use De Morgan's theorem to express the OR in terms of NAND operations: A + BC = (A' (BC)')'. Step 1: Generate A' by using a 2-input NAND with both…
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Correct answer: 3
Key idea: use De Morgan's theorem to express the OR in terms of NAND operations: A + BC = (A' (BC)')'.
Step 1: Generate A' by using a 2-input NAND with both inputs tied to A (this implements NOT A).
Step 2: Generate (BC)' by using a 2-input NAND on inputs B and C.
Step 3: NAND the signals A' and (BC)' to get Y = (A' (BC)')' which equals A + BC.
Therefore the minimum number of 2-input NAND gates required is 3.