The application is an undergraduate electronics lab board. It shows basic A/D concepts and
implements a basic FIR filter. I tried coding it in assembly, but the math never came out quite right.

Hallo Lee,

sounds very interesting. May I ask, what kind of FIR filter you use? How many taps? What wordlength? Is FIR filter self designed or is it a ready solution?
Some years ago, I was involved in a project where someone wanted to implement FIR filter. Result was a little bit strange and it was found out that rounding errors poduced some inconvenience. May be that this is the reason for what you called 'math never came out quite right' ? Only an idea...

Regards,
Kai