Binary Calculator

A simple calculator for performing binary arithmetic operations.

How to use this calculator

Enter two base-2 numbers using only the digits 0 and 1. Choose Add, Subtract, Multiply, or Divide, then select Calculate. The result is written in binary. A number such as 101 is read as a binary value here, rather than the decimal number one hundred and one.

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HOW BINARY PLACE VALUES WORK

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Starting at the right, binary positions represent 1, 2, 4, 8, 16, and successive powers of 2. The value 1011₂ therefore means 8 + 0 + 2 + 1 = 11 in decimal. Leading zeros do not change a positive value: 0011₂ and 11₂ both represent decimal 3.

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WORKED ARITHMETIC EXAMPLES

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Addition: 101₂ + 11₂ = 1000₂, which is decimal 5 + 3 = 8. Multiplication: 101₂ × 10₂ = 1010₂, or decimal 5 × 2 = 10. Division: 110₂ ÷ 10₂ = 11₂, corresponding to decimal 6 ÷ 2 = 3. Check your work by converting the inputs and output to decimal.

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CARRYING AND INTERPRETING RESULTS

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In binary addition, 1 + 1 = 10₂: write 0 in the current position and carry 1 to the next. This is the same place-value idea as carrying in decimal, but the base is 2 rather than 10.

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Do not enter digits from 2 to 9 or divide by zero. This arithmetic tool does not let you choose a fixed register width or a signed encoding such as two’s complement, so do not interpret its output as an 8-bit or 16-bit processor register. Very large values may exceed numerical precision; use a dedicated arbitrary-precision tool for exact large-integer work.