In order to solve a Boolean equation we need to understand some rules. These rules help us to solve the equation by reducing the terms in equation.
Rule 1: This rule states that if we add a term say 'A' to 1, then we will get 1 as result
A + 1 = 1.
Rule 2: If we multiply a term with 1, we get A as a result.
1A = A.
These are identity rules.
Rule 3: If we add a term to its complimented form then we get 1 as a result.
A + A’ = 1,
Rules 4: If we have an equation as (A + B) (A + C) then we can represent it as (A + BC). This is called product of sum expression.
Rule 4: If we have an equation as A + A’B then can be written as A + B.
A + A’B = A + B.
Now let us take an example understand the process of finding solution of a Boolean expression.
Assume that we have a Boolean equation (A + B) (A + C), we can reduce this equation as:
We can see that it is a product of sum expression. We will apply rules on this expression. First we will multiply the terms:
AA + AC + AB + BC.
Applying the identity rule on AA = A.
A + AC + AB + BC,
Applying the rule A + AB = A,
A + AB + BC.
Applying the rule A + AB = A
A + BC. This is the solution of Boolean equation.