Binary Calculator
1010 + 0011 = 1101, which is 13 in decimal. Use this binary calculator to add, subtract, multiply, or divide two binary numbers and see the answer in both binary and decimal right away. Enter only 0s and 1s, choose the operation, and the tool converts each input from base 2 into decimal, runs the arithmetic, then converts the result back to binary for display. That makes it useful for homework checks, coding practice, logic design review, and quick sanity checks when you want to confirm what a binary expression means without working through every carry or borrow on paper.
Quick answer
Each input must contain only binary digits, so valid entries look like 1010, 0011, or 111111.
What this tells you
- •Each input must contain only binary digits, so valid entries look like 1010, 0011, or 111111.
- •Leading zeros are allowed. 0011 and 11 represent the same value, but the extra zeros can make manual checking easier.
- •The result card shows the computed answer in binary and decimal, plus the decimal value of each input.
- •Division returns the integer quotient only. If the decimal answer would include a fraction or remainder, this tool rounds down by taking the whole-number quotient.
How to Use
- 1Enter the first binary number in Binary A. Enter only 0 and 1 digits with no spaces or prefixes.
- 2Enter the second binary number in Binary B. Use leading zeros if you want the numbers lined up for hand-checking, but they are optional.
- 3Choose Add, Subtract, Multiply, or Divide depending on the binary math problem you want to solve.
- 4Click Calculate to view the binary result, the decimal result, and the decimal interpretation of each input.
- 5If you are checking your own work, compare the decimal version first. It is often the fastest way to catch a carry, borrow, or division mistake.
How It Works
Formula
Parse binary to decimal -> apply arithmetic -> convert the result back to binaryBinary place values double as you move left, so 1010 means 1×8 + 0×4 + 1×2 + 0×1 = 10. This tool first parses each binary input into its decimal value, then applies the chosen operation. After that, it converts the decimal result back into a base-2 string for the main answer. For division, the tool returns the integer quotient by taking the whole-number result. For negative subtraction results, the decimal answer stays negative while the binary output follows the tool's current 32-bit unsigned JavaScript conversion behavior.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Binary addition
1010 is 10 in decimal and 0011 is 3. Adding them gives 13, which is 1101 in binary. This is the basic pattern for checking carries in base-2 addition.
Binary subtraction
1101 is 13 and 0010 is 2. Subtracting gives 11, which converts back to 1011. This is a clean example for practicing binary borrowing without crossing into a negative result.
Binary multiplication
0110 is 6 and 0011 is 3. Multiplying gives 18, which is 10010 in binary. This mirrors the repeated-shift idea behind binary multiplication because 6×3 equals 6 + 12.
Binary division
1111 is 15 and 0010 is 2. The exact decimal result would be 7.5, but this tool returns the integer quotient only, so the displayed answer is 7, which is 111 in binary.
Common Binary Values
A quick lookup table for powers of two and a few common small binary numbers.
| Binary | Decimal | Why it matters |
|---|---|---|
| 0001 | 1 | The smallest non-zero bit value |
| 0010 | 2 | 2¹, useful for place-value checks |
| 0100 | 4 | 2², common in bit masks and shifts |
| 1000 | 8 | 2³, the first place value in a 4-bit nibble |
| 1111 | 15 | All four low bits set |
| 10000 | 16 | 2⁴, the next value after 1111 |
Every step left doubles the value. That doubling pattern is the core of base-2 arithmetic.
How binary math works in practical terms
Binary arithmetic looks strange at first because there are only two digits, but the logic is simpler than it seems. Each column can hold 0 or 1. Once a column would exceed 1, you carry into the next place. So 1 + 1 becomes 10, which means 0 in the current place and 1 carried into the twos place.
That carry pattern is why decimal checking helps. If 101101 feels abstract, read it as 32 + 8 + 4 + 1 = 45. Once you know the decimal meaning, it is easier to confirm whether addition, subtraction, or multiplication landed in the right neighborhood. The tool shows both forms so you can move between the machine-friendly version and the human-friendly version without switching calculators.
Division is where expectations usually drift. This tool does not show a remainder field or a fractional binary expansion. It takes the whole-number quotient only. That keeps the result practical for many programming and logic exercises, but it also means 1111 ÷ 0010 returns 111 because the decimal quotient 7.5 is cut down to 7.
One more detail matters if you subtract into a negative answer. The decimal output stays negative, which is easy to read. The binary output follows the tool's current unsigned 32-bit conversion behavior, so a negative result is shown the way JavaScript converts that signed integer into bits. That is useful to know if you were expecting a signed fixed-width classroom format instead.
Common mistakes
- Entering prefixes like 0b1010 or separators like spaces. This calculator accepts plain binary digits only.
- Expecting division to show a remainder or fractional binary output. It returns the integer quotient only.
- Assuming leading zeros change the value. They do not. 00101 and 101 both equal 5.
- Confusing a negative decimal result with signed binary input support. The tool can display a negative decimal answer after subtraction, but it does not accept signed binary notation as input.
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