Question

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

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

Better step by step process please.

Answer 1

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

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

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

F(A,B,C,D)= C'D[(A' + A)(B' + A)] + CD { By Distributive law P+QR = (P+Q)(P+R) }

​​​​​​​ F(A,B,C,D)= C'D[(1)(B' + A)] + CD { We know that P+P'=1 }

​​​​​​​ F(A,B,C,D)= C'D(B' + A) + CD

​​​​​​​ F(A,B,C,D)= B'C'D + AC'D + CD { By Distributive law P(Q+R) = PQ+PR }

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

​​​​​​​ F(A,B,C,D)= B'C'D + [(A + C)(C' + C)]D { By Distributive law P+QR = (P+Q)(P+R) }

​​​​​​​ F(A,B,C,D)= B'C'D + [(A + C)(1)]D  { We know that P+P'=1 }

​​​​​​​​​​​​​​ F(A,B,C,D)= B'C'D + AD + CD { By Distributive law P(Q+R) = PQ+PR }

​​​​​​​​​​​​​​ F(A,B,C,D)= B'C'D + CD + AD

​​​​​​​​​​​​​​​​​​​​​ F(A,B,C,D)= D(B'C' + C) + AD

​​​​​​​​​​​​​​​​​​​​​ F(A,B,C,D)= D[(B' + C)(C' + C)] + AD { By Distributive law P+QR = (P+Q)(P+R) }

​​​​​​​​​​​​​​​​​​​​​ F(A,B,C,D)= D[(B' + C)(1)] + AD  { We know that P+P'=1 }

​​​​​​​​​​​​​​​​​​​​​​​​​​​​ F(A,B,C,D)= B'D + CD + AD  { By Distributive law P(Q+R) = PQ+PR }

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

Which is required Simplified Expression

Given F = AD + B'D + CD

[F']' = [(AD + B'D + CD)']'

F = [(AD)' (B'D)' (CD)']'

NAND Gate Circuit: