Learning · Step 2

Q-format basics

Fixed point drops the per-number exponent. A Q-format number is just a plain integer — you decide, once, where the binary point sits. Store the integer i; it stands for the real value i / 2^Q, where Q is how many bits you put after the point.

A signed N-bit word splits into 1 sign bit, some integer bits, and Q fractional bits. Q15 in an int16_t is the classic: 1 sign + 15 fractional bits, covering [−1, 1) in steps of 2−¹⁵. Move the point left (smaller Q) for more range; right (bigger Q) for finer resolution — you can't have both.

Converting in is just rounding: i = round(x × 2^Q), clamped to the word. Converting out is i / 2^Q. There's no exponent to rescale per sample — that's what makes fixed point fast, and what makes choosing Q the whole game.

Try it

Slide the binary point with Q, switch the word width, click bits, or type a value — the decode, range, and resolution update live.

Q 15 Value

Presets:

What to notice

Slide Q up — the binary point moves right, the step size (LSB) shrinks, but the range collapses toward [−1, 1). That trade-off is the whole reason to think about Q.
Type 0.1 — just like in a float it can't land exactly; the quantization error is shown.
Type 1.0 at Q15 — it saturates: the largest Q15 value is 1 − 2−¹⁵, just short of 1.
Set Q = 0 — the point is at the far right and the format is a plain signed integer again.

Step exam

Answer all 3 questions correctly to complete this step.

What does the "15" in a Q15 format count?
For a 16-bit Q15 value, what is the resolution (one LSB)?
What is the approximate range of a signed Q15 value?