Page 23 - Computer_Science_F5

Computer Science Simplification using Boolean laws
There are different ways used to simplify Boolean expressions. These include the
use of the laws of algebra and the Karnaugh map (K-map). This textbook will cover
only simplification using the laws of Algebra.

FOR ONLINE READING ONLY
Example 1.1
Using the laws of Boolean algebra, simplify the following expression: (A+ B).(A+C).
Procedure:
(A+B).( A+C)=
= A.A+ A.C+B.A+ B.C -Distributive law

= A+A.C +B. A+ B.C -Idempotent AND law (A.A = A)
= A(1+ C)+ B.A+B.C -Distributive law
=A+ B.A +B.C -Annulment OR law (1 + C = 1)
= A(1+ B)+B.C -Distributive law
= A.1+ BC. -Annulment OR law (1 + B = 1)
= A+BC. -Identity AND law (A.1 = A)

Example 1.2

Using laws of Boolean algebra, simplify the following expression: ABC+ A+ AB

Procedure:
ABC + AB + ABC= ABC + ABC + AB - Commutative law
= AB(C + C) + AB - Distributive law
= AB.1 + AB - Complimentary law
= AB + AB - Identity AND law (A.1 = A)
= A(B + B) - Distributive law
= A.1 - Complementary law
= A - Identity AND law (A.1 = A)

Exercise 1.2 (b) BC + BC + AC

1. Prove the following using Boolean (c) B + AB + ABC
laws and rules: (d) ABC + AC + ABC
(a) AB+AC +ABC = AB +AC (e) AC + ABC
(b) A (A + B) = AB (f) ABC D + ABCD

2. Use laws of Boolean algebra to 3. Using the laws of Boolean algebra,
simplify the following expression. verify the Boolean identity

(a) ABC + ABC +( ⋅ )= A+(A⋅B)=A

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for Advanced Secondary Schools

Computer Science Form 5.indd 14 23/07/2024 12:32