Base Radix Converter & Multi-Base Number Calculator (Base 2 to 36

Positional Number Systems, Radix Bases (2 to 36) & Bit Grouping

A positional numeral system represents numbers using digits multiplied by powers of the base (radix B):

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• Positional Expansion Formula**:

N = Σ_k=0^n-1 d_k · B^k = d_n-1 B^n-1 + + d_1 B^1 + d_0 B^0

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• Common Computing Number Bases**:

• Base 2 (Binary): Digits \0,

• The fundamental language of digital silicon transistors.

• Base 8 (Octal): Digits \0..

• Groups 3 binary bits; used in Unix file permissions (chmod 755).

• Base 10 (Decimal): Digits \0..

• Universal human standard.

• Base 16 (Hexadecimal): Digits \0..9, A..F. Groups 4 binary bits; used in memory addresses, color hex codes (#FFFFFF), and byte buffers.

• Base 36 (Alphanumeric): Digits \0..9, A..Z. Case-insensitive human-readable URL tokens and database IDs.

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• Standard Computing Powers of 2**:

• 2^8 - 1 = 255 = 0xFF = 1111\ 1111_2 1 Byte Max

• 2^16 - 1 = 65,535 = 0xFFFF 16-bit Unsigned Word Max

• 2^32 - 1 = 4,294,967,295 = 0xFFFFFFFF 32-bit IPv4 / Integer Max

How to Use This Calculator

Enter your Input Number / String (e.g. 255 or FF or 11111111), From Base (Source Radix) — choose from Base 2 (Binary - 0, 1), Base 8 (Octal - 0 to 7), Base 10 (Decimal - 0 to 9), To Base (Target Radix) — choose from Base 2 (Binary), Base 8 (Octal), Base 10 (Decimal), and Computer Science & Math Benchmark — choose from Custom Radix Conversion, Decimal 255 (8-bit max) → Binary: 11111111, Hex: FF, Octal: 377, Hex 0xDEADBEEF → Decimal: 3,735,928,559 (32-bit magic number). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Conversion factors (to SI base unit or reference unit):

src: 10

tgt: 16

Worked Example

A software engineer configuring an 8-bit hardware timer register converts the decimal value 255 into hexadecimal 0xFF and binary 1111 1111, confirming all 8 register bit flags are set to high (1).

Understanding Your Result

Chemical calculations require careful attention to significant figures — your result is only as precise as your least precise input. For laboratory work, verify that temperature, pressure, and concentration conditions match the formula's assumed standard state (typically 25°C and 1 atm). Compare your result against published reference values for the specific compound or reaction. Safety note: laboratory chemical calculations should always be verified by a qualified chemist before practical application.