Question 1

What is Qm.n fixed-point notation?

Accepted Answer

Qm.n is a fixed-point notation where m is the number of integer bits (including the sign bit for signed formats) and n is the number of fractional bits. The total word length is m + n bits. So Q1.15 means 1 integer bit (the sign) + 15 fractional bits = 16 bits total, often abbreviated Q15. Q1.31 = 32 bits total (a.k.a. Q31). The fractional bits give a resolution (quantum) of 2^-n — Q15 has a resolution of 1/32768 ≈ 3.05e-5.

Question 2

What is the difference between signed Qm.n and unsigned UQm.n?

Accepted Answer

Signed Qm.n uses two's-complement encoding for the integer bits, so the most-significant bit is the sign bit. The representable range is [-2^(m-1), 2^(m-1) - 2^-n]. Unsigned UQm.n has no sign bit and uses all m integer bits for magnitude, giving a range of [0, 2^m - 2^-n]. The tool supports both — toggle the Signed checkbox to switch.

Question 3

What rounding and overflow modes are supported?

Accepted Answer

Three rounding modes: round-half-up (the schoolbook rule, ties go away from zero), round-to-nearest-even (the IEEE 754 default, ties go to the even LSB — eliminates bias), and truncate (floor toward negative infinity for signed, toward zero for unsigned). Two overflow modes: saturate (clamp to the representable range with an overflow warning) and wrap (two's-complement wraparound, the default CPU behavior).

Question 4

What are the quantization error and resolution readouts?

Accepted Answer

Resolution (quantum, LSB weight) = 2^-n and is shown as both a fraction and a decimal. The quantization error is the exact difference between your typed real value and the value reconstructed from the stored integer — it is computed with BigInt so it is exact to the last digit, never a re-printed float. For rounding modes the error is bounded by ±0.5 LSB; for truncate it is in [-1, 0] LSB (signed) or [-1, 0] LSB (unsigned).

Question 5

What extra features does this tool have versus other Q-format converters?

Accepted Answer

(1) Both signed Qm.n AND unsigned UQm.n with a single toggle (most assume signed only). (2) Three rounding modes (round-half-up, round-to-even, truncate) — most only do one. (3) Two overflow modes (saturate vs wrap) with an explicit warning flag. (4) Live resolution (2^-n) as both fraction and decimal. (5) Live representable range display. (6) Exact quantization error via BigInt (not a re-printed float). (7) Raw stored integer in decimal, hex, and binary simultaneously. (8) Clickable bit grid with integer | fraction bit split color-coded. (9) Q7 / Q15 / Q31 / Q1.15 / Q1.31 / UQ8.8 / UQ16.16 preset chips. (10) Real → Q and Q → real both directions. (11) History (localStorage, last 20). (12) Shareable URL with full state round-trip. 100% client-side and offline — your values never leave the device.

Fixed-Point Q-Format Converter (Qm.n)

Format info

Q1.15

How to use

Format info

Q1.15