Design of a divide-by-N asynchronous odd-number counter with 50/50 duty cycle

Methods of designing an asynchronous divide-by-N odd-number counter with 50/50 duty-cycle output are presented. The counter can be implemented by an EXCLUSIVE OR gate associated with a divide-by-(N + 1)/2 counter and a flip-flop, or by the combination of EXCLUSIVE OR gates and flip-flops.