Question

Simplify the following functions, and implement them with two-level NAND gate circuits:

(a) F (A, B, C, D) = AC'D' + A'C + ABC + AB'C + A'C'D'

(b) F (A, B, C, D) = A'B'C'D + CD + AC'D

(c) F (A, B, C, D) = (A' + C' + D') (A' + C') (C' + D')

Answer 1

a)

SIMPLIFICATION

F (A, B, C, D)
= AC'D' + A'C + ABC + AB'C + A'C'D'
= AC'D' + A'C'D' + A'C + ABC + AB'C [Associative Law]
= (A+A')C'D' + A'C + (B+B')AC [Distributive Law]
= (1)C'D' + A'C + (1)AC [Inverse Law]
= C'D' + A'C + AC [Null Law]
= C'D' + (A'+A)C [Distributive Law]
= C'D' + (1)C [Inverse Law]
= C'D' + C [Null Law]
= D' + C [Absorption Law]

NAND Circuit

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