Binary Calculator
Perform arithmetic on binary numbers — add, subtract, multiply and divide values written in base 2. Each result is shown in binary, decimal, and hexadecimal so you can cross-check against other tools.
Enter binary numbers
Enter two binary numbers and an operation.
Binary arithmetic rules
Binary addition
| Bits | Sum | Carry |
|---|---|---|
| 0 + 0 | 0 | 0 |
| 0 + 1 | 1 | 0 |
| 1 + 0 | 1 | 0 |
| 1 + 1 | 0 | 1 |
| 1 + 1 + carry | 1 | 1 |
Binary multiplication
Multiply the multiplicand by each bit of the multiplier, then add the partial products. Since the multiplier bits are 0 or 1, each partial product is either zero or a shifted copy of the multiplicand.
Binary subtraction
Subtract bit by bit, borrowing 2 from the next higher position when needed.
For example, 1010₂ − 0011₂ = 0111₂ (10 − 3 = 7).
Binary division
Binary long division is analogous to decimal long division, but the quotient digits are only 0 or 1. This calculator reports the quotient and remainder for integer division.
Worked examples
Example 1 — Addition
1010₂ + 0011₂ = 1101₂
In decimal: 10 + 3 = 13.
Result: 1101₂ (13)
Example 2 — Multiplication
110₂ × 101₂ = 11110₂
In decimal: 6 × 5 = 30.
Result: 11110₂ (30)
Example 3 — Division
1100₂ ÷ 0010₂ = 0110₂
In decimal: 12 ÷ 2 = 6.
Result: 110₂ (6)
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Frequently asked questions
Binary uses only two digits (0 and 1), so when you add 1 + 1 you get 2, which in base 2 is written as 10 — a "1" in the twos column and a "0" in the ones column.
Multiply each bit by its positional power of 2 and sum. For 1101₂: 1·8 + 1·4 + 0·2 + 1·1 = 13.
This calculator works with unsigned binary numbers. Subtraction that would produce a negative result returns an error. Signed binary systems (two's complement, sign-magnitude) are outside the scope here.