Simplify the following expressions using Boolean Algebra :-
- A + AB
= A.1+AB
= A(1+B) :- OR (A+1 = 1)
= A.1
= A
- AB+AB’
= A(B+B’) :- AB+AC = A(B+C)
= A(B+B’) :- A + A’ =1
= A(1)
= A
- A’BC + AC
= C(A’B+A) :- A+BC = (A+B).(A+C)
= C((A’+A).(A+B)) :- A’+A=1
= C(1.(A+B))
= C(A+B)
- A’B+ABC’+ABC
= A’B+AB(C’+C) :- A’+A=1
= A’B+AB
= B(A’+A) :- A’+A=1
= B
- A’ B’ C + A’ B C’ + A B’ C’ + A B C
= A’(B’C+BC’)+A(B’C’+BC) :- A’B+AB’ = A XOR B , A’B+AB’ = (A XOR B)’
=A’(B XOR C) + A((B XOR C)’) :- let B XOR C = T , A’T+AT’ which implies =A XOR T
= A XOR T :- T = B XOR C
=A XOR B XOR C
Note: It is illustrated for beginners
