Why are the absorption laws also called redundancy laws?
The correct answer and explanation is :
The Absorption Laws in Boolean algebra are also called Redundancy Laws because they help eliminate redundant terms in logical expressions. These laws simplify Boolean expressions by demonstrating that certain terms do not affect the final outcome and can be removed without changing the logic.
Absorption Laws:
- A + (A · B) = A
- Here, the term A · B is redundant because if A is 1, the result is already 1 due to A alone. If A is 0, the result remains 0 regardless of B.
- A · (A + B) = A
- In this case, the term A + B is redundant because if A is 1, the result remains 1 regardless of B. If A is 0, the result is 0.
Why Are They Called Redundancy Laws?
- Elimination of Extra Terms:
- These laws show that certain terms in an expression do not contribute to the final result and can be removed, making the expression simpler.
- Optimization of Logic Circuits:
- In digital circuit design, removing redundant terms reduces the number of logic gates, saving cost, power, and improving efficiency.
- Logical Justification:
- The additional term does not provide any new information or effect on the output, making it redundant.
Example:
Consider an expression:
X + (X · Y) = X
If X = 1, the result is 1 regardless of Y.
If X = 0, the result is 0 regardless of Y.
Thus, the term X · Y does not affect the output and is redundant.
By recognizing and applying these laws, Boolean expressions become more efficient and easier to work with.