Binary Calculator

Perform binary arithmetic free online. Add, subtract, multiply, and divide binary numbers, with decimal and hex equivalents shown for every value and result.

Browser only.

How to Use This Tool

Enter two binary numbersType values using only 0s and 1s

Choose an operationPick add, subtract, multiply, or divide

Read the resultSee binary, decimal, and hex equivalents

Arithmetic at the Level Computers Actually Operate

Every calculation a computer performs ultimately happens in binary, regardless of which decimal numbers you see on screen. For most everyday computing, this layer stays invisible -- but for computer science students learning processor architecture, or developers debugging code involving bitwise operations and flags, working directly in binary builds an understanding that purely decimal thinking can't provide.

This calculator performs the four basic arithmetic operations directly on binary input, showing the result simultaneously in binary, decimal, and hexadecimal so you can verify your understanding against a familiar reference point.

Two's Complement -- The Standard for Negative Numbers

When binary subtraction produces a negative result, this calculator represents it using two's complement notation, the same convention virtually all modern processors use internally. Understanding two's complement -- where the leading bit indicates sign and negative numbers wrap around in a specific predictable pattern -- is a foundational concept in any computer architecture course.

Why Hex Exists as a Middle Ground

Binary is precise but unwieldy for humans to read -- an 8-bit byte is 8 characters long. Hexadecimal compresses that same information into 2 characters while preserving an exact, clean mapping to the underlying bits (each hex digit corresponds to exactly 4 bits), which is why programmers reach for hex constantly when binary precision matters but readability also matters.

Frequently Asked Questions

Computer science students learning how processors handle arithmetic at the bit level, anyone debugging low-level code involving bitwise operations, or electronics hobbyists working with binary-coded logic circuits all encounter situations where seeing the actual binary arithmetic matters more than just the decimal result.

This calculator shows results using standard two's complement representation for negative numbers, which is how virtually all modern computer hardware represents negative integers internally -- understanding this representation is foundational for anyone studying computer architecture.

All three represent the exact same underlying numeric value using different bases -- binary (base 2), decimal (base 10) which is what humans normally use, and hexadecimal (base 16) which programmers favor because it maps cleanly to binary (each hex digit represents exactly 4 binary bits).

A byte (8 bits) in binary is a long string like 11010110, while the same value in hex is just D6 -- two characters instead of eight. Hex preserves the clean mapping to binary bits while being far more compact and readable for humans.

Standard JavaScript number precision handles binary values well into the range needed for typical educational and debugging purposes, covering far more than the 8, 16, or 32-bit values most commonly encountered in coursework or everyday low-level debugging.