Binary Calculator
Perform binary arithmetic and bitwise operations with ease. Supports +, -, *, /, AND, OR, XOR.
🔢 Binary Inputs
How to Use Binary Calculator
Follow these simple steps to get the best results.
Enter binary numbers
Type two binary numbers (0s and 1s) that you want to perform arithmetic on.
Choose operation
Select addition, subtraction, multiplication, or division for the binary calculation.
View binary and decimal results
See the result in both binary format and its decimal equivalent side by side.
Frequently Asked Questions
Everything you need to know about Binary Calculator.
About the Binary Calculator Tool
Perform complex arithmetic on binary numbers with the ToolFlic Binary Calculator. Binary math is the foundation of computer science; our tool allows you to add, subtract, multiply, and divide binary strings (base-2) with the same ease as standard decimal calculations.
Core Advantages
Master the fundamentals of digital logic and computer architecture. This tool is an invaluable resource for students and developers who need to verify their binary calculations or perform low-level data manipulation. It's professional-grade, fast, and completely free.
Architecture & Security
Our engine uses a high-performance bit-manipulation algorithm that processes binary strings natively. It handles signed and unsigned carry operations with expert precision, providing a clean and accurate result for even the most complex binary math.
Under the Hood: the Binary Calculator explained properly
No marketing filler — just the mechanics, the trade-offs and the real limits, explained clearly.
How it actually works
Both operands are checked against a strict 0/1 pattern and then handed to JavaScript BigInt through the 0b literal form, so the arithmetic is exact at any length you can type. Addition, subtraction, multiplication, division, AND, OR and XOR are the seven operations, all evaluated on full integers rather than on a fixed 32-bit word.
The answer is written in three notations at once: binary, decimal and hexadecimal, each with its own copy action, plus a bit-length readout measured on the magnitude. A division returns the integer quotient, truncated toward zero, and dividing by zero is refused with a message in the error line instead of producing Infinity or a silent wrong number.
What that means for your results
Because BigInt has no fixed width, there is no overflow cliff. A 64-bit mask, a 128-bit value or a 400-bit product all come back correct, which is what makes the tool usable for real bit-field work such as permissions flags, network headers or file-format offsets.
Bitwise operators are defined on two's complement, and that is what you get, including for results of subtraction that went negative. A negative answer is displayed as a minus sign followed by the magnitude, not as a 64-bit wrapped pattern, so read the decimal field when the sign matters.
Where it falls short — honestly
Numbers are unsigned on the way in. There is no two's-complement entry mode, no word-size selector and no way to ask for the result as exactly 8, 16 or 32 bits, so the tool will not show you how a value is laid out inside a struct or a register.
Whitespace, separators and a stray 2 are rejected with a per-field message, which is helpful for a typo and annoying for a 4,000-bit string pasted with line breaks. Shift operations are not offered here; for shifting, masking and 0x-prefixed input in one place use Hex Calculator.
A real end-to-end workflow
Typical jobs are verifying a flag layout and checking a hand-summed offset: does 1000000 + 100000 give the seventh and sixth bits as intended, does the AND with 11111111 strip a length byte the way the format document claims, does the XOR of two checksum halves produce the expected value.
Work from the widest field down: confirm the decimal interpretation first, then read the binary result against the spec, then copy the hexadecimal form into your source. If you need the same number as text rather than as arithmetic, Binary to Text converts bit groups back to characters.
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