Digital Electronics And Logic Gates

Concept: A MOD-N counter requires a number of flip-flops such that: where is the number of flip-flops.
Step 1: Given MOD value.

Step 2: Find minimum .

Step 3: Conclusion.
Thus, 4 flip-flops are required.

Concept: In Boolean algebra, the principle of duality states that every algebraic expression remains valid if operators and identity elements are interchanged.
Step 1: Duality principle.
To find the dual:

• Replace OR (+) with AND ( )
• Replace AND ( ) with OR (+)
• Replace 0 with 1 and 1 with 0

Step 2: Apply to OR operation.
The dual of OR is AND.
Step 3: Example.

Step 4: Conclusion.
Thus, the dual of the OR operation is AND.