**[u]T flip-flop[/u]**[edit]

A circuit symbol for a T-type flip-flop
If the T input is high, the T flip-flop changes state ("**[u]toggles[/u]**") **whenever the clock input is strobed**. If the T input is low, the flip-flop holds the previous value. This behavior is described by the characteristic equation:
Q_{next} = T \oplus Q = T\overline{Q} + \overline{T}Q (expanding the XOR operator)
and can be described in a truth table:

"T" stands for TOGGLE. (hence the name, duh)

BTW, not that it matters any more but your post title doesn't match your problem. You were looking for a frequency divider , which is quite different from simple inversion, as suggested by your post title.
I'm just sayin'.....