Question

computer organazation , Boolean algebra

1. Show the Boolean algebra reduction to minimal form for each. Show each step, and cite the rule number which allows it.

a . (AB)’ (A’ + B) (B’ + B)

b . A’(A+B) + (B + A)(A + B’)

Answer 1

a. 
(AB)’ (A’ + B) (B’ + B)
= (AB)’ (A’ + B) (1)
= (AB)’ (A’ + B)
= (A' + B') (A’ + B)
= A'A' + B'A' + A'B + B'B
= A' + B'A' + A'B + 0
= A' + B'A' + A'B
= A' (1 + B' + B)
= A' (1 + 1)
= A'


b.
A’(A+B) + (B + A)(A + B’)
= (A’A+A'B) + (B + A)(A + B’)
= (0+A'B) + (B + A)(A + B’)
= A'B + (B + A)(A + B’)
= A'B + (BA + AA + BA + BB')
= A'B + (BA + A + BA + BB')
= A'B + (BA + A + BA + 0)
= A'B + (BA + A + BA)
= A'B + (BA + A)
= A'B + A(B + 1)
= A'B + A(1)
= A'B + A