Use the properties and theorems of Boolean Algebra to reduce the following expression to OR-AND expressions. The expressions may not be unique, but create a truth table that is unique to the expression. (a'bc + a)
Properties for reducing the Boolean expression:
De-Morgan’s Law:
(A+B)’= A’.B’ and (A.B)’=A’+B’.
Complement Law for Addition:
A+A’=1
Identity Law of Multiplication:
(A.1)=A
Dominant Law of Addition:
(1+A)=1
Idempotent Law of Multiplication:
(A.A)=A
Compliment Law of Multiplication:
(A.A’)=0
Solution:
For the given Boolean expression (a'.b.c+a) can be reduced as follows.
=(a'.b.c+a)
= (a+a’.b.c)
Let, bc=x,
=(a.1+a'x) Hence, A.1=A
=[a.(1+x)]+a'.x Hence, 1+A=1
=(a.ax)+a'.x
=(a.a+a.x)+a'.x Hence, A.A=A
=a.a+a.x+a.a'+a'.x Hence, A.A'=0
=a.(a+x)+a'.(a+x)
=(a+a').(a+x) Hence, A+A'=1
=(a+x)
Placing the value of x=bc,
=(a+bc)
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