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Binary Calculator
Add, subtract, multiply and divide binary numbers, or apply AND, OR and XOR. Results are shown in binary, decimal and hex, with the working.
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A binary calculator performs arithmetic directly on base-2 numbers. For example, 1011 + 110 = 10001 in binary, which is 11 + 6 = 17 in decimal.
How to use the binary calculator
- Enter the first and second binary numbers.
- Choose an operation: add, subtract, multiply, divide, AND, OR or XOR.
- Read the answer in binary, decimal and hex, and open the steps to check the working.
Examples
| Operation | Binary | Decimal check |
|---|---|---|
| 1011 + 110 | 10001 | 11 + 6 = 17 |
| 1101 – 101 | 1000 | 13 – 5 = 8 |
| 101 x 11 | 1111 | 5 x 3 = 15 |
| 1100 / 11 | 100 | 12 / 3 = 4 |
| 1100 AND 1010 | 1000 | 12 AND 10 = 8 |
| 1100 OR 1010 | 1110 | 12 OR 10 = 14 |
| 1100 XOR 1010 | 110 | 12 XOR 10 = 6 |
Binary arithmetic rules
Addition
| Sum | Result |
|---|---|
| 0 + 0 | 0 |
| 0 + 1 | 1 |
| 1 + 0 | 1 |
| 1 + 1 | 10 (write 0, carry 1) |
| 1 + 1 + 1 | 11 (write 1, carry 1) |
Example: 1011 + 0110. Work from the right, column by column, carrying a 1 whenever a column adds up to two or more. The result is 10001.
Subtraction
Subtract bit by bit and borrow from the next column when you need to take 1 from 0. A shortcut is to add the two’s complement of the number being subtracted.
Multiplication and division
Binary multiplication is shift and add: for each 1 in the multiplier, add a copy of the multiplicand shifted left. Division is long division with only two possible quotient digits, 0 and 1.
Bitwise operators
| A | B | AND | OR | XOR |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 |
Bitwise operators are used for flags, masks and permissions in programming. For negative numbers see the two’s complement calculator.
Binary calculator FAQ
Can it handle negative results?
Yes. A subtraction that goes below zero shows a leading minus sign.
How large can the numbers be?
There is no fixed limit; arbitrary-precision integers are used.
What does XOR mean?
XOR gives 1 when the two bits are different and 0 when they are the same.
What is 1 + 1 in binary?
It is 10, which is 2 in decimal.
Can I check the answer in decimal?
Yes, the decimal value of every result is shown.