Page 40 - Digital Electronics by harish

1.4.4 Simplification of expression using Boolean techniques

We can simplify logic expressions using Boolean techniques (ie.)Boolean laws and theorems.

Example 1 : Simplify the expression Y = A + A B

Y = A + A B
= A ( + B) …. By factoring
= A (1) ….. + B = 1
= A ….. A . 1 = A

Example 2 : Simplify the expression Y = B + AB + ABC

Y = B + AB + ABC
= B + AB + AB + ABC … AB + AB = AB
= B(+A) + AB(+C) …. By factoring
= B + AB …. +A = 1

Example 3 : Simplify the expression Y = AB + + AC(AB+C)

Y = AB + + AC(AB+C)
= AB + + AABC + ACC …. Multiply
= AB + + 0 + AC …. B = 0, CC = C
= AB + + + AC …. DeMorgan‟s theorem = +
= AB + + + AC …. Rearrange
= AB + + + C …. Distributive law
= + AB + + C …. Rearrange
= + B + + …. Distributive law
= + + B + …. Rearrange
= + + 1 …. B + B’ = 1
= 1 ….. Reduce

1.4.5 Boolean expression for outputs

The following steps are involved to find out the boolean expression for the output of the
given logic circuit.
Step 1 : Label all the inputs ie. A, B, C, D, etc.
Step 2 : Label all the gates in the circuit ie. A1, A2, A3, A4, etc.
Step 3 : Start with the input signals, write down the logic equation for the output of each
gate until the output is reached.

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