Simplification of Boolean Expression | Physics4students
By manipulating a Boolean expression according to laws and theorems of Boolean algebra, a simple expression that will require fewer gates, can be obtained. To see how Boolean algebra manipulation is used to simplify digital circuits, let us consider the following example. In the circuit given, the outputs of the OR gates are A compliment or B, and A or B. These are the inputs for the AND gate and the output of the circuit is Y is equal to A compliment or B, and A or B.
Now using the distributive law twice, we can write
A compliment or B, and A or B is equal to A compliment and A, or A compliment and B, or B and A, or B and B.
Since A compliment and A is equal to zero and B and B is equal to B
That is equal to A compliment and B or A and B or B.
Since A compliment or A or one is equal to one.
That is equal to B and A compliment or A or one is equal to B.
Since the output of the circuit is simply B, we don’t need a logic circuit.
