A T flip-flop toggles its output at the active clock edge when T equals:

Concept

A T flip-flop is a one-bit memory element whose next state depends on the input T and the present state Q.

Its characteristic relation is Q(next) = T XOR Q. One input condition retains Q, while the other complements Q.

Application

1. Substitute T = 1 in the characteristic relation: Q(next) = 1 XOR Q = NOT Q.

2. Thus the next output becomes the complement of the present output, which is the toggling action.

Contrast

• For T = 0, Q(next) = 0 XOR Q = Q, so the stored state is retained.

• For T = 1, Q(next) = 1 XOR Q = NOT Q, so the stored state is complemented.

• The two binary input values therefore do not produce the same action, so they cannot both be toggling conditions.

• The characteristic relation defines an action for each binary input, so excluding both inputs is inconsistent with the device behavior.

Cross-check

Starting from Q = 0 gives Q(next) = 1; starting from Q = 1 gives Q(next) = 0. The state changes in both cases when T = 1.

Hence the T flip-flop toggles when T = 1.