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The task of designing a circuit for powering on a device with a push button switch instead of a latching switch is surprisingly complex.

The simple part is the NMOS feedback circuit that keeps the device powered on after releasing the switch.

The hard part is turning the switch into an off button after it has been released the first time.

I think what I need is a T flip-flop, and I've constructed one in a simulator out of MOSFETs, but I'm having some trouble getting it to work properly.