Worked example

Operation: Decimal → bits
a: -1
Bit width: 8

→ 1111 1111; hex: FF; 10: −1

Method and scope

Encode a signed decimal integer or decode an exact-width binary string (without spaces). The leading bit is the sign bit. Range: −2^(w−1) to 2^(w−1)−1. Out-of-range values are rejected, never silently wrapped.

negative x → 2ʷ + x

Precision and limits

≈ marks an approximation. Display rounding does not change the internal calculation.