Base Converter

Base Converter is evaluated from Number to Convert, From Base and To Base. The calculation reports Result, Decimal Intermediate and Digits Used.

Results

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About the Base Converter

Base Converter is treated here as a quantitative relation between Number to Convert, From Base and To Base and Result, Decimal Intermediate, Digits Used and Place Values.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
To decimal: sum of (digit x base^position)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

To decimal: sum of (digit x base^position)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Base 5 to Decimal — Math Contest

Inputs

value: 2314 from_base: 5 to_base: 10

Result: 334. Decimal Intermediate: 334. Digits Used: 0-9. Place Values: 2314 (base 5) = 334 (base 10) = 334 (base 10)

With Number to Convert = 2,314, From Base = 5 and To Base = 10 as the stated inputs, the result is Result = 334, Decimal Intermediate = 334 and Digits Used = 0-9. Each value corresponds to the declared output fields.

Example 2: Hex to Binary — Network Mask

Inputs

value: FFFF0000 from_base: 16 to_base: 2

Result: 11111111111111110000000000000000. Decimal Intermediate: 4294901760. Digits Used: 0-1. Place Values: FFFF0000 (base 16) = 4294901760 (base 10) = 11111111111111110000000000000000 (base 2)

With Number to Convert = FFFF0000, From Base = 16 and To Base = 2 as the stated inputs, the result is Result = 11111111111111110000000000000000, Decimal Intermediate = 4294901760 and Digits Used = 0-1. Each value corresponds to the declared output fields.

Example 3: Base 36 — URL Shortener Code

Inputs

value: XK2F from_base: 36 to_base: 10

Result: 1565655. Decimal Intermediate: 1565655. Digits Used: 0-9. Place Values: XK2F (base 36) = 1565655 (base 10) = 1565655 (base 10)

With Number to Convert = XK2F, From Base = 36 and To Base = 10 as the stated inputs, the result is Result = 1565655, Decimal Intermediate = 1565655 and Digits Used = 0-9. Each value corresponds to the declared output fields.

Example 4: Base 12 (Duodecimal) — Dozens

Inputs

value: 100 from_base: 12 to_base: 10

Result: 144. Decimal Intermediate: 144. Digits Used: 0-9. Place Values: 100 (base 12) = 144 (base 10) = 144 (base 10)

With Number to Convert = 100, From Base = 12 and To Base = 10 as the stated inputs, the result is Result = 144, Decimal Intermediate = 144 and Digits Used = 0-9. Each value corresponds to the declared output fields.

Common Use Cases

Convert between any number bases for programming
Learn positional notation systems
Convert base 36 encoded strings
Explore number theory concepts