Math

Number System Converter

Convert Between Any Positional Number Systems

A positional numeral system represents numbers using digits weighted by powers of the base. This converter supports all standard bases (binary, octal, decimal, hex) plus arbitrary bases from 2 to 36.

Number Base Conversion Tips

Click to show tips

Try an Example

Pick a scenario to see how the calculator works, then adjust the values

ASCII Letter A

Convert the ASCII code for uppercase A (65) across all bases.

Key values: Decimal 65 · Binary 1000001 · Hex 41

Byte Maximum

The largest value a single byte can hold (255).

Key values: Decimal 255 · Binary 11111111 · Hex FF

Hex Color Code

Convert a common hex color code (deep sky blue) to other bases.

Key values: Hex 00BFFF · Decimal 49151 · Binary nibbles

Documentation

This calculator is also known as Number System Converter.

Read the complete guide

Positional Numeral Systems

In a positional system, each digit's value depends on its position. The number 345 in base 10 means 3*100 + 4*10 + 5*1. The same principle applies to any base.

Examples

Base 5 Conversion

Convert 1234 in base 5 to decimal.

1*125 + 2*25 + 3*5 + 4*1 = 194.

Key takeaway: 1234 in base 5 equals 194 in decimal.

Base 36 Conversion

Convert the base-36 string "HELLO" to decimal.

H(17)*36^4 + E(14)*36^3 + L(21)*36^2 + L(21)*36 + O(24) = 29234652.

Key takeaway: Base 36 can encode alphanumeric strings as numbers, useful for compact identifiers.

Octal to Hex

Convert Unix permission 755 (octal) to hexadecimal.

755 octal = 493 decimal = 1ED hex.

Key takeaway: Octal and hex are both power-of-2 shorthand for binary (3 and 4 bits per digit).

Understanding Number Systems

Key concepts for working with different number systems:

All conversions route through decimal (base 10) as an intermediary
Bases that are powers of 2 (2, 4, 8, 16) have shortcut conversions via bit grouping
The digit alphabet for bases > 10 extends with A-Z (A=10 through Z=35)

Frequently Asked Questions about Number System Converter

Why are bases 2, 8, 10, and 16 the most common?

Base 10 comes from counting on 10 fingers. Base 2 maps to electronic on/off states. Bases 8 and 16 are compact shorthand for binary (3 and 4 bits per digit respectively).

Can I convert directly between two non-decimal bases?

The converter routes all conversions through decimal (base 10) internally. You enter a value in any base, and it converts to decimal first, then to all other bases.

What bases beyond 16 are actually used in practice?

Base 32 is used in Crockford encoding and geohashing. Base 36 is used for compact alphanumeric identifiers (YouTube video IDs, short URLs). Base 64 is common for encoding binary data in text.