Binary Numbers & Logic

Binary Calculator

Add, subtract, multiply, or divide signed binary integers.

Binary Numbers & Logic

Enter binary or code values

Deterministic local calculation with explicit word sizes and conventions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Prefixes 0b, 0o, and 0x are accepted where a field says “integer”. Underscores and visual spacing are ignored where appropriate. Your values stay in this browser.

Binary result

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

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Understand the subject

What is binary arithmetic?

Binary uses place values that double from right to left, so its arithmetic follows the same place-value idea using only 0 and 1.

Use it to calculate exact signed base-two integers.

The rule

Read the representation exactly

See the structure

What the bits are doing

Worked interpretation

Read the result in context

0+0=0; 0+1=1; 1+1=10₂

Interpret with care

Important boundary

This calculator works with integers; a binary point needs the separate fraction tool.

For a small base-two example, use the Binary Calculator.

Quick guide

How to use this calculator

  1. Choose the direction, operation, representation, or parity convention when one is provided.
  2. Enter the labelled values and an explicit word size, base, polynomial, or encoding option where required.
  3. Read the primary result together with its alternate representations and stated convention.

Calculation method

Apply the declared binary rule

Base-2 arithmetic follows the same place-value rules as decimal arithmetic.

The calculator validates every digit against its numeral base, keeps integer and bitwise work exact with arbitrary-precision integers, and limits fixed-width operations to the selected word.

Worked example

Worked binary example

1011₂ + 110₂ = 10001₂.

Base-2 arithmetic follows the same place-value rules as decimal arithmetic.

Supported inputs

Precision and limits

Input interpretation

Binary-only fields accept 0 and 1. General integer fields accept decimal plus 0b, 0o, or 0x prefixes. Base conversion supports bases 2 through 36.

Word size and output

Most fixed-width tools support 1–256 bits. Results expose signedness, truncation, parity, or encoding conventions whenever those choices change the meaning.

Local privacy

Calculation runs in the browser. Entered text, bit patterns, code words, and numeric values are not sent to analytics or third parties.