How can a flip flop alternate between two clocks, turning one off and the other on and repeating?

How can a flip flop alternate between two clocks, turning one off and the other on and repeating?

I am just experimenting with flip flops and am pretty confused about alternating between two clocks. Right, so I want a pulse to be sent to a flip flop first after 18 seconds and then after 2 seconds and then again after 18 seconds. For this purpose, I have made two 555 timer ICs which generate 18s and 2s pulses respectively. What I have been struggling to do is to, after the 18s timer IC generates a pulse, activate the 2s timer IC and deactivate the 18s timer IC and after the 2s timer IC generates the pulse, I would like to deactivate it and activate the 18s timer IC. What I want I want the flip flop to get a pulse after 18seconds, then after 2 seconds, then after 18 seconds and then 2 seconds and so on. Any help would be greatly appreciated.

Probably, the most simple way to produce the clocking signal you need is to produce a single clock Q with a period of 20ms and a 90 duty cycle: by inverting such clock for example by using a NOT gate or a single fast transistor inverter you will get another clock overlineQ with the same period but with a 10 duty cycle. Each of this waveform is shown below: Then, the original clock signal will provide the 18ms pulse, while the inverted one will provide the 2ms, for example by the following simple RCD trigger circuit: simulate this circuit Schematic created using CircuitLab By calling t_1 the trigger generated by feeding Q to the input the of the above circuit and t_2 the one generated by overlineQ, these signals have waveforms similar to the following ones: Few notes You can use one 555 to generate Q and then inverting its output: however the simplest way is perhaps to generate both Q and overlineQ by a single, properly designed, astable multivibrator. The RCD trigger circuit show above is simply an analog differentiator: R and C control the duration of the trigger pulse, while D rules out the negative pulse which would otherwise appear during the falling of the input squared wave signal.