# Number encodings at a glance: from base-b to floating point

> Every number representation at a glance: base-b, binary, ones and twos complement, bit operations, excess-q, fixed and floating point, each with a calculator.

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

Binary, 1-complement, 2-complement, excess-q, fixed-point, floating-point, b-adic and bitops with fine-grained Horner steps and bit-level visualisation.

## Topics

- [B-adic / Horner method](https://marckimmel.de/en/informatik/zahlenkodierungen/b-adisch.md): Interactive b-adic representation: Horner conversion with fine-grained division and remainder steps, polynomial form, switch between any bases 2..36.
- [Binary Encoding](https://marckimmel.de/en/informatik/zahlenkodierungen/binaer.md): Interactive n-bit binary encoding: Horner conversion step by step, bit visualisation, value range, addition with carry and overflow.
- [One's Complement](https://marckimmel.de/en/informatik/zahlenkodierungen/einerkomplement.md): Interactive n-bit ones' complement: negation by flipping all bits, double zero, a range symmetric around zero, −127 to 127 with 8 bits.
- [Two's Complement](https://marckimmel.de/en/informatik/zahlenkodierungen/zweierkomplement.md): Interactive n-bit two's complement: negation by flipping all bits plus one, unique zero, asymmetric value range. Standard for int8 to int32.
- [Bitwise Operators](https://marckimmel.de/en/informatik/zahlenkodierungen/bitops.md): Interactive bitops: column-wise NOT, AND, OR, XOR and shifts on two n-bit patterns. With per-column truth pills and result bit pattern.
- [Excess-q](https://marckimmel.de/en/informatik/zahlenkodierungen/exzess-q.md): Interactive excess-q encoding: stores x as x + q in n bits. Used in IEEE 754 characteristics (bias 127 for float, 1023 for double).
- [Fixed-point](https://marckimmel.de/en/informatik/zahlenkodierungen/festkomma.md): Interactive fixed point with n bits and k fractional digits: multiplication by a power of two, rounding, Horner conversion, rounding error and value range.
- [Floating-point](https://marckimmel.de/en/informatik/zahlenkodierungen/gleitkomma.md): Interactive floating-point encoding: sign, characteristic (excess-q) and mantissa step by step, with bit visualisation and rounding error.

## Related

- [Computer science](https://marckimmel.de/en/informatik.md)