Fixed Number Formats

[@p_mouse8676]

Why 4 bits is 2^4 but 24 bits isn't 2^24 is very unclear at this point and not really explained? 🤔🥴

[@HowtoSigmaDSP]

Thanks so much for taking the time to ask a question. It is difficult to lecture just looking at myself looking back at me! There are a few things I could have explained better for sure. My simple example was actually five bits. The sign bit and then the factional part that was four bits. A 24 bit number has one sign bit and 23 factional bits. One other thing I did NOT mention was that for the Sigma300/350 cores since one bit is added to the bottom, you use 2^24 not 2^23. A 24 bit number is really ONLY a fractional number. You have one sign bit and 23 fractional bits. If you think of it like 0dBFS you will see it is only a number between 0 and almost 1. I have another video coming hopefully tonight where I discuss level.

[@p_mouse8676]

@@HowtoSigmaDSP thanks! 😊 Just to see if I understand it well. Let's say we have a hypothetical 27 bit system, with one sign bit and 6 whole bits, this leaves us with 27-1-6=20 fraction bits left? Also, with the default 5.23 system, (like the adau17/1401 etc), I assume that the max headroom also comes from those whole bits? Since 20*log(15)=24dB

[@HowtoSigmaDSP]

Hello p_mouse, Yes! you got it. The 27 bit example you used would be a 7.20 format so 20 bits would be the fractional part. About the max headroom. Yes, four bits x 6dB/bit = 24dB. This is the topic of my next video I recorded a couple of days ago and I am editing right now. So you are making great connections and jumping ahead!