Learning · Step 3

Pick Q for your data

Q15 was a choice, not a law. Q is set by your data: you need enough integer bits to hold the largest value you'll ever see, and every bit you don't spend on the integer side becomes resolution. Pick Q wrong and you either overflow or throw away precision.

Measure your data's peak — the largest magnitude max|x|. The integer side must reach at least that far; the rest is fraction. The best Q is the largest one whose range still covers the peak: maximum resolution, no overflow.

Too much Q → the integer range is smaller than the peak → values saturate. Too little Q → integer bits sit unused while resolution is coarser than it needed to be. The app's Q auto-suggest tool does this measurement for you; the explorer below shows what it's deciding.

Try it

Set your data's peak, slide Q, switch the word width — the bit budget recolours and the verdict updates live.

Data peak (max|x|) Q 15

integer — needed integer — spare fraction overflow

Example peaks:

What to notice

Raise Q past the suggestion — the integer side gets too small and the data overflows (the budget turns red).
Lower Q below the suggestion — it still fits, but the dim spare bits are wasted: you could have had finer resolution.
The suggested Q sits right at the edge — every integer bit earns its place, every other bit is resolution.
Try peak 400, then 0.05 — the right Q swings wildly with your data's range. That's why you measure the data first.

Step exam

Answer all 3 questions correctly to complete this step.

Your data's largest magnitude is 12. The Q-format's integer side must:
Choosing too large a Q — too many fractional bits — for your data causes:
The best Q for a dataset is: