T flip-flop

Also called: toggle flip-flop, T flip flop, T-type flip-flop, TFF, T-FF

An edge-triggered flip-flop with one input T: at each active clock edge it toggles Q if T = 1 and holds Q if T = 0. Q⁺ = T ⊕ Q.

A T flip-flop has a single input, T, which answers one question at each rising clock edge: should Q change?

T never says what Q should become, only whether it flips. Its characteristic equation is Q⁺ = : XOR with 1 inverts, XOR with 0 passes through.

Why it matters:

With T held at 1, Q flips every edge, so it runs at half the clock frequency. That is a frequency divider.
In a binary counter, each bit flips exactly when all lower bits are 1. T flip-flops express that directly: Tᵢ is the AND of the lower bits. That is why counters are often designed with them.

You rarely buy a T flip-flop as a part. Instead you make one: tie J and K of a JK flip-flop together as T, or drive a D flip-flop with D = .

A quick shortcut: count the edges where T = 1. An even count leaves Q where it started; an odd count leaves it flipped.

Worked examples

Example

Q starts at 0. Rising edges are in slots 2, 4, 6, 8 and 10.

Example

A T flip-flop starts at Q = 0. T is held at 1 for 23 rising edges. What is Q afterwards?

Interactive questions with instant feedback and a worked solution for every wrong answer.

And 2 more in the Counters lesson.

T flip-flop is taught in Latches and Flip-Flops and Counters.