Binary Calculator

What is a binary calculator?

A binary calculator performs arithmetic directly on two base-2 integers. Binary numbers use only 0 and 1, but addition, subtraction, multiplication, and division follow the same basic ideas as decimal arithmetic.

This calculator keeps Binary as the primary result and also shows Decimal and Hex equivalents. It handles integers up to 4,096 bits with browser-native large integer arithmetic.

How to use the binary calculator

1. Enter the first binary integer in Operand A.
2. Select Add, Sub, Mul, or Div.
3. Enter the second binary integer in Operand B.
4. Read the Binary, Decimal, and Hex results, which update automatically.

You can enter plain binary digits, use a 0b prefix, or group digits with spaces or underscores. For example, 0b1010_1010 and 1010 1010 represent the same value. Negative and fractional inputs are not supported.

The calculator opens with the example values loaded. After you edit either operand, the result updates 300 milliseconds after you stop typing.

Binary calculation example

101101 + 11011 = 1001000

The same calculation in decimal is:

45 + 27 = 72

Binary arithmetic rules

Binary addition

Binary addition carries when a column reaches two. The key rule is 1 + 1 = 10, so you write 0 and carry 1 to the next column.

Binary subtraction

Binary subtraction borrows from the next column when subtracting 1 from 0. If Operand B is larger than Operand A, the result uses an ordinary minus sign, such as 101 - 111 = -10.

Binary multiplication

Binary multiplication uses only 0 × n = 0 and 1 × n = n. Shifted partial values are added to form the result.

Binary division

Binary integer division returns a quotient and a remainder. It does not produce a fractional binary expansion.

Binary and decimal values

Binary arithmetic uses base 2 instead of base 10. A binary digit’s place value is a power of two, so 1011 means 8 + 2 + 1, which equals 11 in decimal.

The result shows separate Binary, Decimal, and lowercase Hex values. Hex values include a 0x prefix, such as 0x48.

Understanding binary division results

The quotient is the whole-number result of the division. The remainder is the amount left over after that whole-number division.

For example:

1110 ÷ 100 = 11 remainder 10

This is 14 ÷ 4 = 3 remainder 2 in decimal. A divisor of zero is invalid.

Binary calculator FAQ

What operations can the binary calculator perform?

It performs binary integer addition, subtraction, multiplication, and division.

Can I use a 0b prefix or grouped digits?

Yes. The calculator accepts an optional 0b or 0B prefix, spaces, and underscores. Results are returned as ungrouped binary digits.

Can binary subtraction produce a negative result?

Yes. A negative result uses a normal minus sign. This is ordinary signed arithmetic, not a two’s complement representation.

What happens when dividing binary numbers?

The calculator displays an integer quotient and remainder. The second operand cannot be zero.

Does the calculator support very large binary numbers?

Yes. It uses native BigInt arithmetic and accepts up to 4,096 binary digits per operand, avoiding the precision limit of JavaScript Number values.

Is a binary calculator the same as a binary converter?

No. A binary calculator performs arithmetic on two binary values. A binary converter changes one value between binary and another number system.

What is the difference between binary arithmetic and bitwise operations?

Binary arithmetic calculates numeric values with +, −, ×, and ÷. Bitwise operations such as AND, OR, XOR, NOT, and shifts manipulate individual bit positions and require separate rules for width and signed values.