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Binary and Decimal Base Converter — result sheet
Convert a nonnegative whole number between binary notation and decimal notation while keeping every bit visible.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Binary value = sum(bit × 2^position); decimal-to-binary repeatedly divides by 2 and reads remainders from last to first.
Binary is a positional system with two symbols. The rightmost bit represents 2^0, the next represents 2^1, and so on. Decimal-to-binary conversion reverses that weighted-sum process without rounding a fractional value.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Value — Use only 0 and 1 for binary input, or decimal digits for decimal input.
- Conversion direction — 2 choices
Worked example
| Input | Value |
|---|---|
| Value | 101101 |
| Conversion direction | binary-to-decimal |
45
Assumptions and limits
- The value is a nonnegative whole number; fractional binary values are outside this tool's scope.
- Binary strings are limited to 53 bits so decimal output remains exactly representable in JavaScript number formatting.
- Leading zeroes are accepted and do not change the numeric result.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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