Circuits / Sequential
T Flip-Flop Frequency Divider
Toggles Q between 0 and 1 on each rising clock edge when T = 1, dividing the clock frequency by two.
A T (Toggle) Flip-Flop flips its stored bit Q (~Q) on the rising edge (0 → 1 transition) of Clock (CLK) whenever its Toggle input T is 1, and holds Q steady when T is 0.
Its characteristic equation is Q(next) = T ⊕ Q. Because Q changes state only once per full clock period (on the rising edge), tying T = 1 makes output Q oscillate at exactly half the frequency of CLK.
This divide-by-2 behavior is the foundation of binary ripple counters and synchronous up-counters: chaining N T Flip-Flops divides the input clock by 2^N and counts from 0 to 2^N - 1.
In this circuit T starts at 1. Each pair of Tick clicks completes one full clock cycle and toggles Q once.
Tip: Keep T = 1 and click Tick repeatedly: Q flips only on the 0 → 1 rising clock edge, dividing the clock frequency by 2.