Do arithmetic and bitwise operations on binary numbers.
Add column by column, carrying when 1 + 1 = 10. 1011 + 110 = 10001 (11 + 6 = 17 in decimal).
Binary is the base-2 number system used by computers: only the digits 0 and 1. This calculator adds, subtracts, multiplies and divides binary numbers (with quotient and remainder), applies the bitwise operators AND, OR and XOR, and shows every answer in binary, octal, decimal and hexadecimal. A second tool converts any number between bases.
All arithmetic uses exact big-integer maths, so very long binary numbers work. For base-16 work see the Hex Calculator; for huge decimal numbers the Big Number Calculator; for IP addresses the IP Subnet Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Binary (base 2) | 10001 |
| Octal (base 8) | 21 |
| Decimal (base 10) | 17 |
| Hexadecimal (base 16) | 11 |
| Base | First number | Second number |
|---|---|---|
| Binary | 1011 | 110 |
| Octal | 13 | 6 |
| Decimal | 11 | 6 |
| Hexadecimal | B | 6 |
| Operation | Result |
|---|---|
| 1011 + 110 | 10001 |
| 1011 − 110 | 101 |
| 1011 × 110 | 1000010 |
| 1100 AND 1010 | 1000 |
| 1100 XOR 1010 | 110 |
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 17 | 10001 | 21 | 11 |
| 18 | 10010 | 22 | 12 |
| 19 | 10011 | 23 | 13 |
| 20 | 10100 | 24 | 14 |
Add from the right; 1 + 1 gives 0 with a carry of 1 to the next column.
Multiply each bit by a power of 2 (from the right) and add. 1011₂ = 8 + 2 + 1 = 11.
Subtract bit by bit, borrowing from the next column when you need to take 1 from 0.
AND gives 1 only if both bits are 1; OR gives 1 if either is 1; XOR gives 1 if the bits differ.
Yes, with a leading minus sign for arithmetic. Bitwise operations need non-negative numbers.
Electronic circuits have two reliable states — on and off — which map to 1 and 0.
It uses the standard method: decimal = Σ bit × 2ᵏ e.g. 1011₂ = 8 + 0 + 2 + 1 = 11 The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
