hi billy,
using 4 diodes is called rectification, using only 1 is half wave (i think)
to answer your question they part you are mainly looking for is a counter, plus you need to generate pulses, which is 555 timer suggested, finally you need logic to decode the garble (binary) out of the counter...also this logic feeds back to the reset pin....and/or/not gates and such. and a pile of wire
you could also do it with shift registers and flip flops,
there are lots of funny little chips out there and ways you could do it and you do not seem to be a student , but someone looking for answers to practical problems, and if you are getting in to tracing pulses and decoding data i suggest skipping HARDWARE logical circuits, and jump over to a micro controller,
i have not picked up a logic IC since, for example the 12f510 is the same size, and a rather small processor but can do 10x more, then you can count AND log many pulses with a simple 10 lines of code. and reprogram it when you made a mistake and realize that it was the 24th pulse you had to switch with...
I would suggest for you to cut to a chase here, where r u coming from and where are you going with these pulses??
if you explain what you are doing exactly you will be more likely properly pointed in a correct direction... usually small questions like these will send you barking up the wrong tree.