fixed-point arithmetic

**Fixed-Point Arithmetic** is a **number representation system where the decimal point is at a fixed position** — contrasting with floating-point where the exponent shifts the decimal. It is the mathematical foundation underpinning quantized neural network inference. **What Is Fixed-Point?** - **Format**: $Q(m, n)$. $m$ integer bits, $n$ fractional bits. E.g., $Q(3,4)$: $0101.1100 = 5.75$. - **Operations**: Addition/subtraction are trivial. Multiplication requires shifting to realign the decimal. - **Trade-off**: Fixed range (no exponent) means less dynamic range but deterministic precision. **Why It Matters** - **Hardware Cost**: Fixed-point multipliers are 5-10x smaller/cheaper than floating-point on ASICs/FPGAs. - **Determinism**: Bit-exact reproducibility across platforms (critical for safety-certified systems). - **DSP Heritage**: All digital signal processing (audio, communications) has used fixed-point for decades. **Fixed-Point Arithmetic** is **silicon-friendly math** — the number system that makes neural network inference affordable on the cheapest chips.