A binary counter to count upto 100 (decimal) needs at least

Concept:

• For ‘n’ number of flip-flops, a binary counter will have 2ⁿ different states and this counter is said to be “ MOD-2ⁿ ” counter.
• A binary flip-flop would be capable of counting up-to (2ⁿ - 1) before returning to zero state.
• The “MOD-number” indicates the number of states in counting sequence and frequency division obtained from last flip-flop.

Calculation:

For counting upto 100 (decimal) minimum number flip-flop required can be calculated as

100 < (2ⁿ - 1)

For n = 7, we get

100 < (2⁷ - 1)

100 < 125

Hence at least 7 flip-flops required for counting up-to 100.