# Excess-q (biased) visualised: characteristic with bias q

> Interactive excess-q encoding: stores x as x + q in n bits. Used in IEEE 754 characteristics (bias 127 for float, 1023 for double).

Address: https://marckimmel.de/en/informatik/zahlenkodierungen/exzess-q
Deutsche Fassung: https://marckimmel.de/informatik/zahlenkodierungen/exzess-q.md

Encodes integers with a fixed bias q. Lexicographically sortable bit patterns.

Excess-q encoding c_(EX-q,n) adds a fixed bias q to the number before encoding it in binary. Bit patterns then sort lexicographically in the same order as the encoded values, allowing hardware comparisons without decoding. For floating-point use one picks q = 2^(n-1) - 1 for a symmetric range. Range: -q to 2^n - 1 - q.

Used in floating-point encoding c_(GK,k,n) for the exponent (IEEE 754: float bias 127, double bias 1023).

## Related

- [Number Encodings](https://marckimmel.de/en/informatik/zahlenkodierungen.md)