Appendix 1: Six ways to divide a Clock (by 2)
It has been found that it is frequently the case that when constructing a circuit one needs a clock divider. However depending on the gates or flip-flops that are "spare" one can find several ways of using what is available.
Using just J-Ks
Often when one takes their first course in Electronics, one is often taught to use J-K flip-flops in order to divide a clock. These two circuits show two alternative ways of dividing a clock (In) by two (Out). Both of these circuits function perfectly well, however in high speed circuits consideration needs to be given to voltage skew in the former case: the voltage at J and K may differ from R and S, but in the latter case the leads connecting Q to K and Q to J may be high speed "wires" which could cause other problems.
The D-type Method
Most modern designs use something more akin to this D-type method for dividing the clock because D-types require fewer transistors during their construction. This is similar to the second J-K method using feedback loops from the output.
The following method is uses only four 2-input gates. This is one of the simplest ways one can implement the function using gates:
Using only a pair of transistors it is possible to make a bistable multivibrator that switches on a negative-going signal on the input. This circuit uses the fewest number of transistors possible (without cheating). Most chips probably silently use something similar to this owing to these facts, such as huge counters, digital watches and so on. Modern chips probably use a similar design, but with Field Effect Transistors instead.
This final version is a bit of hack, but might be useful in the long run... It uses two inverters to maintain the state - when the system starts up the two compete to determine which one will be the ruling party. This is pretty much the gate version of the "Plain Transistors" version above, but uses transistors to permit entry, which could be replaced with diodes if required.