Binary Calculator – Add, Subtract, Multiply, Divide & Convert Binary/Decimal

Binary Calculator & Converter

Perform binary operations (addition, subtraction, multiplication, division) and convert between binary and decimal values instantly. Perfect for computer science students, developers, and anyone working with binary systems.

Binary Operations

First Binary Number

Second Binary Number

Binary Result:

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Decimal Result:

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How to use:

Enter two binary numbers (0s and 1s only)
Select the operation you want to perform
Results will show in both binary and decimal formats

Binary to Decimal

Binary Number

Decimal Value:

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About Binary to Decimal:

Each digit in a binary number represents a power of 2. The rightmost digit represents 2⁰, the next 2¹, then 2², and so on.

Example: 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 11₁₀

Decimal to Binary

Decimal Number

Binary Value:

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About Decimal to Binary:

Conversion is done by repeatedly dividing the decimal number by 2 and recording the remainders. The binary equivalent is the sequence of remainders read from last to first.

Example: 25₁₀ → 25 ÷ 2 = 12 rem 1, 12 ÷ 2 = 6 rem 0, 6 ÷ 2 = 3 rem 0, 3 ÷ 2 = 1 rem 1, 1 ÷ 2 = 0 rem 1 → 11001₂

Understanding Binary Numbers

The binary numeral system is the foundation of all modern computing systems. Unlike the decimal system (base-10) which uses ten digits (0-9), the binary system (base-2) uses only two digits: 0 and 1.

Each digit in a binary number is called a bit. A group of 8 bits is called a byte, which can represent 256 different values (2⁸ = 256). This binary system is used internally by all modern computers because digital circuits have two stable states (on/off, true/false) that naturally represent binary digits.

Binary arithmetic works similarly to decimal arithmetic but with simpler rules since there are only two possible digits. The main operations (addition, subtraction, multiplication, division) follow the same principles as in the decimal system.