The number of flip-flop needed to construct a binary modulo N counter is:

To construct a binary modulo N counter, the circuit must be able to represent at least N distinct states. Since each flip-flop provides 2 possible states (0 or 1), k flip-flops can represent 2^k distinct states. Therefore, the condition is 2^k >= N. Solving for k gives k = ceil(log_2(N)), meaning the number of flip-flops required is the smallest integer greater than or equal to the base-2 logarithm of N.