# Binary Multiplication Calculator URL: https://speedycalculator.com/calculators/math/binary-multiplication/ Last updated: 2026-10-30 > The binary multiplication calculator multiplies two binary numbers with the shift-and-add method, showing the partial products, and gives the product in binary and decimal. ## Inputs - Binary factor 1 - Binary factor 2 - Representation ## Results - Product (binary) - Product (decimal) - Factor 1 in decimal - Factor 2 in decimal - In the chosen bit width - Partial products ## Formula ``` 0 × 0 = 0, 0 × 1 = 0, 1 × 1 = 1; product = sum of shifted copies of A for each 1-bit of B ``` ## Explanation Binary multiplication is simpler than decimal: each partial product is either a copy of the first number or zero. Hardware multipliers add shifted copies in exactly this way. ### How to use the Binary Multiplication Calculator - **Binary factor 1** - **Binary factor 2** - **Representation** Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server. ### How it works Enter two binary numbers. One partial product row is written for each bit of the second number, shifted left by its position, and the rows are added. ## Worked example Inputs — Binary factor 1: 1011; Binary factor 2: 101; Representation: Automatic (fit the numbers). Results — **Product (binary) = 11 0111**; Product (decimal) = 55; Factor 1 in decimal = 11; Factor 2 in decimal = 5; Partial products = 1011 0000· 1011·· ──────── 110111. ## Key terms - **Partial product**: One row of a long multiplication. ## FAQ **What is 1011 × 101?** 110111 (11 × 5 = 55). **How many bits does a product need?** Up to the sum of the bit lengths of the factors. **Why is binary multiplication easy?** Each digit is 0 or 1, so every partial product is 0 or a shifted copy. **How do I multiply by 2 in binary?** Append a 0 (shift left). ## Sources - [Wolfram MathWorld – Binary](https://mathworld.wolfram.com/Binary.html) - [Harvard CS50 – Binary and bitwise operators](https://cs50.harvard.edu/x/)