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Binary Multiplication Calculator

Multiply binary numbers.

How it is calculated

Type two binary numbers in bin1 and bin2, each made only of the digits 0 and 1 and at most 20 digits long. The tool converts both to ordinary integers, multiplies them, and writes the product back in base 2: product = bin1 × bin2. It shows two results, the binary product and its decimal value, which is handy for checking by hand. Leading zeros are accepted and dropped. Anything else is rejected without a message and gives no result: digits 2 to 9, a minus sign, a point, spaces inside the number, or more than 20 digits. Only the final product is shown, not the partial rows of the long multiplication.

Worked example

Multiply 1011 by 110. In decimal these are 11 and 6. Shift-and-add: the digit 0 of 110 contributes nothing, the digit 1 in the twos place contributes 1011 shifted one place, 10110, and the digit 1 in the fours place contributes 1011 shifted two places, 101100. Adding 10110 + 101100 gives 1000010, which the tool also shows as 66 in decimal, matching 11 × 6.

Try this example →

Common mistakes

  • Typing decimal numbers such as 11 and 6. Digits above 1 are rejected, so 102 gives no result; enter 1011 and 110 for those values.
  • Entering a negative binary number with a minus sign or two's complement. Only unsigned 0 and 1 strings are accepted.
  • Forgetting the binary carry when checking by hand: 1 + 1 = 10, not 2. Use the decimal line as a cross-check.
  • Entering numbers longer than 20 digits. The input is limited to 20 binary digits each, and a longer string returns nothing rather than a trimmed answer.

About this calculator

Multiplying two binary numbers follows the same shift-and-add long multiplication method you’d use for decimal numbers, but it is simpler because every digit is either 0 or 1: each partial product is either all zeros or an exact shifted copy of the multiplicand, with no multiplication table to memorize. Those partial products are then added together (with binary carrying) to get the final result, which the calculator also converts to decimal so you can verify it.

This shift-and-add process is exactly how multiplication circuits work at the hardware level inside a CPU’s arithmetic logic unit (ALU) — binary multipliers in silicon are literally built from shifters and adders performing this operation. It is a core topic in computer science and digital logic courses, where students learn binary arithmetic before moving on to how processors implement it in hardware.

Inputs can run up to 20 digits each, and the product appears in both binary and decimal without the partial products listed, so write those out by hand to follow the steps.

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