Script Number Encoding (CScriptNum)

19. Script Number Encoding (CScriptNum)

Overview

All arithmetic opcodes in Bitcoin Script operate on integers encoded in a special format called CScriptNum (named after the C++ class in Bitcoin Core that implements it). Understanding this encoding is essential to correctly reason about any script using arithmetic.

CScriptNum is a little-endian, sign-magnitude variable-length integer encoding. It differs from both standard two's complement (used in most CPUs) and from big-endian encodings.

Encoding Rules

Rule 1: Little-endian byte order
  - Least significant byte comes first

Rule 2: Variable length
  - Use the minimum number of bytes required
  - Leading zero bytes are not allowed (enforced by MINIMALDATA flag)

Rule 3: Sign is encoded in the most significant bit of the LAST byte
  - If the high bit of the last byte is 1, the number is negative
  - If it is 0, the number is positive

Rule 4: Zero is encoded as an empty byte vector
  - [] (empty) = 0
  - Not 0x00 (a single zero byte would be non-minimal)

Encoding Examples

``` Value | Bytes | Notes