Question

You have to design a logical circuit for a 4-bit composite number using K-MAP (SOP minimization). Provide the original and simplified Boolean expressions in SOP form. Covert SOP to POS using the K-Map.

Answer 1

Logic circuit for 4 bit composite number is

$Y=AC+ABC + \bar{A}BC+AB+D$

Simplifying the given boolean function

$Y=AC+ABC + \bar{A}BC+AB+D$

$Y=AC+BC +(A \bar{A})+AB+D$

SOP $\implies Y=AC+BC + AB+D$

POS $\implies Y=(\bar{A}+ \bar{C})(\bar{B}+ \bar{C})(\bar{A}+ \bar{B})(\bar{D})$

Implementation of SOP in a logic diagram

$Y=AC+BC + AB+D$