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Math

Binary Calculator

Calculate with binary integers and see exact binary, decimal and hexadecimal results.

Exact method explained belowEditable inputs
Binary workbench
Binary workbench

Up to 512 input bits. Exact arithmetic with a separate division remainder.

See the method

Enter two binary integers

Runs on your device

Exact integer result

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter binary a, binary b, operation.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

Input reference and sample values

Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.

InputFormat and unitsSample
Binary AEnter text using the format shown in the sample.101101
Binary BEnter text using the format shown in the sample.110
OperationChoose Add / Subtract / Multiply / Integer divide / Bitwise AND / Bitwise OR / Bitwise XOR.Add

Result for these sample inputs

110011
Decimal
51
Hexadecimal
33

A negative result uses a leading minus sign, not a fixed-width two’s-complement encoding.

Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.

The method, explained

Parse unsigned binary operands exactly as integers. Arithmetic uses arbitrary-precision integer operations. Division returns an integer quotient and a remainder; bitwise operations compare aligned bits.

A WORKED EXAMPLE

Using binary a = 101101, binary b = 110, operation = add, the result is 110011. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Unsigned input operands, up to 512 bits each. No fractional binary, implicit bit width, signed overflow or two’s-complement interpretation. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

Why is division sometimes missing a fraction?

This tool performs exact integer division. The remainder is displayed separately; it does not truncate an unlabelled approximate fractional result.

How is this different from a base converter?

A base converter changes the notation of one number. This calculator performs arithmetic or bitwise operations on two binary inputs and then presents the result in three bases.

Methodology maintained by ClarityKit. How these tools are built and checked.