Binary Calculator
Arithmetic & Bitwise Operations
Working With Binary Numbers
Binary is the native language of digital computing — every value a computer stores or moves is ultimately a string of 0s and 1s. This calculator lets you add, subtract, multiply, and divide binary values, and also perform the bitwise logic operations used directly in low-level code.
Add, subtract, multiply, and divide binary numbers exactly as you would decimal numbers — the calculator converts internally, performs the math, and converts the result back into binary.
AND, OR, XOR, and NOT compare or invert bits position by position — the building blocks of digital logic gates, flags, and masks used throughout computer hardware and software.
Why Bit Width Matters
Bits don't carry a fixed length on their own — 101 and 00000101 represent the same decimal value (5), but a bitwise NOT of each gives a very different-looking answer depending on how many bits you consider. Fixing the bit width to 8, 16, or 32 bits before running NOT or a shift keeps the operation well-defined and matches how real hardware registers behave.
Key Takeaways
- Arithmetic and bitwise operations answer different questions. Arithmetic treats binary as a quantity; bitwise treats it as a sequence of independent flags.
- A left shift multiplies by 2 and a right shift divides by 2 for every position shifted — a fast shortcut used throughout low-level programming.
- The decimal equivalent is always shown alongside the binary result, so you can sanity-check your work without switching tools.
Frequently Asked Questions
- Enter the first binary number (Operand A) using only 0s and 1s.
- Choose an operation — arithmetic (add, subtract, multiply, divide) or bitwise (AND, OR, XOR, NOT, left shift, right shift).
- Enter the second binary number (Operand B), unless you selected NOT, which only needs one operand.
- Click "Calculate" to see the binary result along with its decimal equivalent.
Arithmetic operations (add, subtract, multiply, divide) treat binary numbers as ordinary quantities and produce the same result you'd get doing the math in decimal, just expressed in base-2. Bitwise operations (AND, OR, XOR, NOT, shifts) instead act on the individual bits of each number, comparing or moving them position by position — these are the operations used directly in digital logic, flags, and low-level programming.
Bitwise operations like NOT and the shifts are only meaningful within a fixed number of bits, because flipping every bit of a number technically requires knowing how many bits it occupies. The Bit Width selector (8, 16, or 32 bits) sets that fixed width — for example, NOT on 00001010 at 8-bit width gives 11110101, but the same NOT at 16-bit width gives 1111111111110101.
A left shift moves every bit one or more positions to the left, filling the vacated positions on the right with zeros — this is equivalent to multiplying by 2 for every position shifted. A right shift moves every bit to the right, which is equivalent to dividing by 2 (rounding down) for every position shifted. The Shift Amount operand tells the calculator how many positions to move.
This tool is built for performing arithmetic and bitwise operations on binary numbers, not pure base conversion. If you just need to convert a value between binary and decimal without doing any math on it, use our dedicated Binary to Decimal and Decimal to Binary converters instead.
The calculator only accepts the digits 0 and 1 for binary operands and will show a clear error if anything else is entered. Dividing by a binary value equal to zero is also caught and reported as an error rather than producing an incorrect result.