Number Base Converter
Convert a signed integer between bases 2–36 using exact arithmetic. Compare binary, octal, decimal, hexadecimal and base-36 values with place-value steps.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Read each digit in the input base, multiplying the accumulated value by the base before adding the next digit. Repeated division by the output base produces its digits. The implementation keeps the integer exact throughout.
integer magnitude = Σ digit_k × base^k; digits 0–9 then A–Z represent values 0–35
Worked example
255 in base 10 is FF in base 16, 11111111 in base 2, 377 in base 8 and 73 in base 36. The hexadecimal number FF means 15×16 + 15.
Assumptions and input details
Use 1–256 digits, optionally preceded by + or − (keyboard hyphen), with no prefixes, spaces, separators, decimal point or exponent. Letters are case-insensitive. A negative binary result is signed magnitude with a leading minus, not two’s complement or a fixed-width machine representation. Bases must be whole numbers from 2 to 36. The place-value table shows at most the 16 least-significant input positions; the result uses every digit.
References: OpenStax: converting with base systems
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Fraction, counting, number-base and integer-factor results use exact integer arithmetic. Any decimal or percentage display is approximate.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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