fixed-point arithmetic
Fixed-point arithmetic represents fractional numbers using plain integers with an imagined decimal point nailed at a fixed position — so 0.75 might be stored as the integer 12,288 with everyone agreeing the point sits 14 bits from the right (a 'Q14' format). Unlike floating-point, the point never moves, which makes the math nothing more than fast integer add and multiply. The price is a fixed, uniform resolution and a hard ceiling on range.
Why bother in an era of cheap floating-point? In high-volume, battery-powered, or ultra-fast DSP — hearing aids, motor controllers, baseband radios, billions of IoT chips — a fixed-point multiplier is smaller, cheaper, and far more power-efficient than a floating-point unit. The engineer's craft is managing the two hazards it creates: overflow, when a sum exceeds the range and wraps to a wildly wrong value (tamed by saturation or scaling), and quantization noise, the rounding error injected at every step, which sets the system's noise floor.
Floating-point trades the integer's uniform resolution for a sliding one — many bits of precision near zero, fewer at large magnitudes — which is why audio mastering and scientific DSP favour float, while cost- and power-critical embedded DSP still leans hard on fixed-point.