(a) Using Boolean algebra techniques, simplify the following expression step…
(a) Using Boolean algebra techniques, simplify the following expression step by step:
AB + A(B + C) + B(B + C)
(b) Explain the role of distributive law and absorption law in simplifying Boolean expressions. Why are these laws important in designing efficient digital circuits?
Also indicate where the logic diagram should be drawn in your answer.
Attempted by 28 students.
Show answer & explanation
Given expression: AB + A(B + C) + B(B + C)
First apply distributive law:
A(B + C) = AB + AC
B(B + C) = BB + BC
So expression becomes:
AB + AB + AC + BB + BC
Now apply idempotent law (BB = B):
AB + AB + AC + B + BC
Apply repetition law (AB + AB = AB):
AB + AC + B + BC
Apply absorption law (B + BC = B):
AB + AC + B
Again apply absorption (AB + B = B):
B + AC
Thus, simplified expression is:
B + AC
(b)
Distributive law helps in expanding expressions to make hidden terms visible, which allows further simplification. Absorption law reduces redundant terms, eliminating unnecessary logic operations. These laws are important because they minimize the number of gates and inputs in a circuit, reducing cost, power consumption, and improving speed. Efficient simplification leads to optimized digital circuit design, which is essential in real-world applications like processors and embedded systems.