Number Encodings
Binary, 1-complement, 2-complement, excess-q, fixed-point, floating-point, b-adic and bitops with fine-grained Horner steps and bit-level visualisation.
- B-adic / Horner methodInteractive b-adic representation: Horner conversion with fine-grained division and remainder steps, polynomial form, switch between any bases 2..36.
- Binary EncodingInteractive binary encoding c_{2,n}: step-by-step Horner conversion, bit visualisation, value range, addition with carry and bit overflow. Mirrors unsigned types in C.
- One's ComplementInteractive ones' complement c_{1K,n}: negation by flipping all bits, double zero, value range −(2^{n-1}−1) to 2^{n-1}−1. A teaching stepping stone toward two's complement.
- Two's ComplementInteractive two's complement c_{2K,n}: negation = bit flip plus one, unique zero, asymmetric value range, identical addition to unsigned. Standard for int8, int16, int32.
- Bitwise OperatorsInteractive bitops: column-wise NOT, AND, OR, XOR and shifts on two n-bit patterns. With per-column truth pills and result bit pattern.
- Excess-qInteractive excess-q encoding: stores x as x + q in n bits. Used in IEEE 754 characteristics (bias 127 for float, 1023 for double).
- Fixed-pointInteractive fixed-point c_{FK,n,k}: multiplication by 2^{k-1}, rounding, Horner conversion of the rounded integer. With rounding-error analysis and value range.
- Floating-pointInteractive floating-point encoding: sign, characteristic (excess-q) and mantissa (fixed-point) step by step. Three-colour bit visualisation and rounding-error display.