Binary Multiplication Calculator

How Binary Multiplication Works

Binary multiplication uses the same long-multiplication method you would use with decimal numbers, but because binary only has two digits (0 and 1), the rules are much simpler. When you multiply a binary number by 0 the result is 0. When you multiply by 1 the result is a copy of the number unchanged.

For each bit in the multiplier, working from right to left, you write either a row of zeros (if the bit is 0) or a copy of the multiplicand (if the bit is 1). Each successive row is shifted one place to the left compared to the row below it, exactly as in decimal long multiplication. Once all partial products are written, you add them together using binary addition rules: 0+0=0, 0+1=1, 1+1=10 (carry 1), 1+1+1=11 (carry 1).

Worked Example: 1011 × 1101

Using the default values from this calculator:

• Multiplicand: 1011 (decimal 11)
• Multiplier: 1101 (decimal 13)
• Expected result: 11 × 13 = 143, which is 10001111 in binary

The result 10001111 equals 128 + 8 + 4 + 2 + 1 = 143 in decimal, confirming the answer.

Binary Multiplication Rules

Binary multiplication of individual bits follows AND logic: the product of two bits is 1 only when both bits are 1. The complexity arises when carrying during the addition of partial products.

Converting Binary to Decimal

To check your answer, convert the binary result to decimal by multiplying each bit by its positional value (a power of 2) and summing. The rightmost bit is 2^0 = 1, the next is 2^1 = 2, then 2^2 = 4, and so on. For example, 10001111 = 128 + 0 + 0 + 0 + 8 + 4 + 2 + 1 = 143.

Related Calculators

• Essential Calculators: all computer, digital, and converter tools.
• Binary Converter: convert numbers between binary, decimal, hex, and octal.
• Binary to Text Converter: decode binary to ASCII text.
• Binary Hex Octal Decimal Converter: switch between all common number bases.
• Number Base Arithmetic Calculator: add, subtract, and multiply in any number base.

Method: Standard binary long multiplication: for each bit of the multiplier (right to left), form a partial product by ANDing with the multiplicand and shifting left by the bit position, then sum all partial products using binary addition. Inputs are treated as unsigned integers. Conversion to decimal uses the positional value formula: sum of (bit × 2^position) for all bit positions.

This calculator works with unsigned binary integers. Negative numbers (two's complement) and binary fractions are not supported. The maximum supported input is 32 bits per number. For very large numbers, verify the result using the decimal equivalents shown.