No. of Flip flop required for designing synchronous counter having 5 states with counting sequence : 0 = > 1 = > 6 = > 10 = > 4 will be :

Concept:

The number of flip-flops required for a synchronous counter is determined by the highest binary value in the counting sequence. The formula is:

n ≥ log₂(max state value)

where n is the number of flip-flops needed.

Calculation:

Given:

Counting sequence: 0 → 1 → 6 → 10 → 4

Solution:

1. Identify the highest state value in the sequence: 10

2. Convert 10 to binary: 1010 (4 bits)

3. Calculate minimum number of flip-flops:

n ≥ log₂(10) → n ≥ 3.32

Since we can't have a fraction of a flip-flop, we round up to the next integer: n = 4

Verification:

4 flip-flops can represent up to 2⁴ = 16 states (0-15), which covers all required states in the sequence (0,1,6,10,4).

Final Answer:

The number of flip-flops required is 3) 4.