Problem 1: Write the following Boolean expression in POS form: AB’ + A’C’+ABC Pr
ID: 3599612 • Letter: P
Question
Problem 1:
Write the following Boolean expression in POS form: AB’ + A’C’+ABC
Problem 2: Simplify the following Boolean functions, using K-maps: [10 Points]
F(w,x,y,z)=(1,3,6,9,11,12,14)
Problem 3: Find all the prime implicants for the following Boolean functions and determine which are essential: [15 Points]
A. F(A,B,C,D)=(0,2,3,5,7,8,10,11,14,15)
B. F(w,x,y,z)=(0,2,5,78,10,12,13,14,15)
Problem 4: Simplify the following Boolean function F, together with the don’t-care conditions [10 Points]
A. F(x,y,z)=(0,1,4,5,6)d(x,y,z)=(2,3,7)
B. F(A,B,C,D)=(0,6,8,13,14)d(A,B,C,D)=(2,4,10)
Explanation / Answer
Given : Problem 1
F = AB’ + A’C’+ABC
Apply double compliment on both sides
=> (F')' =( (AB' + A'C' + ABC )' )'
apply (A+B)' = (A'B') for all the sum terms
F = ( (AB')'.(A'C')'.(ABC)')'
apply (AB)' = A' + B' for all the product terms
F = ( (A' + B ).(A+C).(A'+B'+C'))'
This is the POS product of sum form