Binary multiplier

A combinational digital circuit that multiplies two binary numbers and produces their binary product. It forms shifted partial products and combines them with logic circuits such as adders.

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Partial product: A value formed by multiplying one digit of one number by one digit of another. Each input-bit pair creates a partial product that contributes at a position determined by its bit weights.
Binary numeral system: A positional numeral system that represents values using powers of two and the digits zero and one. Bit positions encode the place values whose products the circuit must preserve.
Array multiplier: A multiplier architecture that arranges partial-product generation and addition in a regular grid of cells. Its regular layout contrasts with tree-based reduction structures such as Wallace trees.
Digital signal processing: The representation and processing of signals using numerical operations on digital data. Filtering and transforms repeatedly multiply samples by coefficients.
Binary adder: A digital circuit that adds binary numbers and produces a sum, often with a carry output. Adder stages combine the shifted partial products into the final product.
Boolean algebra: An algebraic system for operations on truth values, used to describe and simplify digital logic. Gate-level multiplier designs implement arithmetic through Boolean functions.
Booth multiplication: A signed-digit multiplication method that recodes runs of multiplier bits to reduce the number of partial products. Booth recoding can reduce partial-product rows compared with direct bit-by-bit generation.
Digital signal processor: A processor designed to perform numerical operations efficiently on digitized signals. Its arithmetic datapath commonly includes hardware multiplication for signal workloads.
Half adder: A combinational circuit that adds two bits and outputs a sum bit and a carry bit. The simplest partial-product reductions can use half adders where only two bits meet.
Logic gate: An electronic circuit that performs a Boolean operation on one or more input signals. AND gates generate unsigned one-bit partial products from pairs of input bits.