Not a homework more of a curiosity but I don't know where to post this so...I know how frequency dividers work but how would one multiply lets say by n the clock signal period just using gates? Is it possible? I know EXOR can double it but what about triple or 4x?

 

In theory you could take the output of an XOR-based doubler and run that through another doubler to get 4x. However, depending on the type of doubler you use, you generally get either a highly asymmetric waveform such that another doubler won't work, or you get a waveform whose duty cycle is highly dependent on the frequency and that you need to use delay elements to fix the duty cycle at an acceptable value. If your input clock is always at the same frequency, then this is reasonably doable; but expect to have quite a bit of jitter in your output clock.

The normal way to do frequency multiplication is with a PLL or DLL, but it sounds like that's not what is of interest to you right now.

 

See multiplication=N=5