I'm having a bit of a hard time trying to get my head around binary radix's. Specifically when it comes to use them in a circuit. On their own I can understand them fine. For example, 2s complement, fixed point, BCD etc..
This is where I'm getting confused.
I've been building a FIR filter in VHDL and have come to the point where I have to implement the coefficients. Each coefficient is below 1 and is 9 bits. The numbers are signed fixed point numbers. The first 8 bits are the fractional part with the 9th bit the sign bit / integer bit.
Now my problem is: now that I have chosen a format (say, 8 bits for fractional part of the number), does that mean every other number I choose to input into the system have to follow the same radix? Fixed point with 8 fractional bits?
As what I'm being told is, when you input an impulse response to the filter the output should be each coefficient in order. When I use "0000000001" as the input then yes I do get each coefficient on the output. But I don't understand how. I understand that a '1' is getting clocked through each stage and being multiplied with each coefficient on each clock but it doesn't represent a "1" in the same format or radix as my coefficients. A true 1 would be "0100000000" as the first 8 bits are fractional.
I'm having a hard time getting my head around the number side of system, the structure and how it's supposed to work.
Is there something wrong with my understanding?