I am currently struggling to get a handle on counter ICs. Some of the ones we have covered are 74ALS160, 163, 190, 191, 192, and 193. While I get the idea of synch and asynch loading and clearing - one is with the clock, the other one overrides the clock, I get lost when drawing the waveforms if it is preloaded - what to do with transitory state? In which case is it just a glitch? Some of them go through two states over one clock... Unclear... please any explanation would be welcome

p.s. I tried studying the spec sheets, still don't get beyond the basic understanding of what is synch and what is not. Don't get the loading part.

 

Give this a read. It should show you how the innards work and what the input and output waveforms look like:
http://www.allaboutcircuits.com/vol_4/chpt_11/2.html

Continue down the left column to read up on other counters.