34. T Flip-Flop (Toggle) and Frequency Division
The T (Toggle) Flip-Flop is a simplified version of the JK Flip-Flop, optimized for applications requiring regular state changes, such as counters and frequency division.
Design
The T Flip-Flop is often derived from the JK FF by permanently connecting the J and K inputs together to a single T input (T = J = K).
Characteristic Table
| T | CLK | Q(t+1) | Operation |
|---|---|---|---|
| 0 | $\uparrow$ | Q(t) | Hold |
| 1 | $\uparrow$ | $\overline{Q(t)}$ | Toggle (Change State) |
Application: Frequency Division
If $T$ is held HIGH (T=1), the output $Q$ toggles (flips) on every clock edge. Since it takes two clock pulses for $Q$ to return to its original state, the output frequency $f_{out}$ is half the input clock frequency $f_{clk}$.
$$\text{Frequency Division Ratio} = 2$$
Chaining N T-FFs creates a counter that divides the clock frequency by $2^N$. This is the basis for asynchronous counters (ripple counters).