Binary Numbers & Logic

Number Base Converter

Convert an integer between any two numeral bases from 2 through 36.

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 changes between number bases?

A numeral’s digits are coefficients of powers of its base; the quantity stays the same when its notation changes.

Use it to inspect whole numbers in bases 2 through 36.

The rule

Read the representation exactly

See the structure

What the bits are doing

Worked interpretation

Read the result in context

(dₙ…d₀)₍b₎=Σdᵢbⁱ

Interpret with care

Important boundary

Every digit must be valid for the selected base.

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

The integer value is preserved while its positional digit representation changes.

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

FF₁₆ = 255₁₀ = 11111111₂.

The integer value is preserved while its positional digit representation changes.

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.