Question

Explain De-Morgan’s principle with two steps to reduce a Boolean expression.

Hint:

De Morgan’s laws convert OR operations into AND operations under negation and vice versa.

Answer 1

Step 1: Understand Boolean Algebra.
Boolean algebra is used in digital logic and computer systems to simplify logical expressions.
It works with binary values such as 0 and 1 (False and True).
Step 2: De Morgan’s Laws.
De Morgan’s principles are used to simplify complex Boolean expressions.
There are two important De Morgan’s laws:
\[ (A + B)' = A' \cdot B' \] \[ (A \cdot B)' = A' + B' \] These laws show how negation distributes over AND and OR operations.
Step 3: First example.
Consider the expression \[ (A + B)' \] Using De Morgan’s law:
\[ (A + B)' = A'B' \] Step 4: Second example.
Consider the expression \[ (A \cdot B)' \] Applying the law gives:
\[ (A \cdot B)' = A' + B' \] Step 5: Conclusion.
Thus De Morgan’s laws help simplify Boolean expressions and are widely used in digital circuit design and logical computations.