Here are two examples of bistable flip flops which can be toggled
between states with a single push button. When the button is pressed,
the capacitor connected to the base of the conducting transistor will
charge to a slightly higher voltage. When the button is released, the
same capacitor will discharge back to the previous voltage causing the
transistor to turn off. The rising voltage at the collector of the
transistor that is turning off causes the opposite transistor to turn
on and the circuit remains in a stable state until the next time the
button is pressed and released. Note that in the LED circuit, the base
current from the conducting transistor flows through the LED that
should be off, causing it to illuminate dimly. The base current is
around 1 mA and adding a 1K resistor in parallel with the LED
will reduce the voltage to about 1 volt which should be low enough
to ensure the LED turns completely off.
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