Number Base Converter

Number Base Conversion

Number base conversion (also called radix conversion) is the process of changing the representation of a number from one positional numeral system to another. Computers use binary (base 2), humans use decimal (base 10), and programmers frequently work with hexadecimal (base 16) and octal (base 8).

Common Number Bases

Base	Name	Digits Used	Common Use
2	Binary	0, 1	Computer hardware, bit manipulation
8	Octal	0–7	Unix file permissions (chmod)
10	Decimal	0–9	Everyday arithmetic
16	Hexadecimal	0–9, A–F	Colors, memory addresses, MAC addresses
32	Base32	0–9, A–V	Encoding, TOTP secrets
36	Base36	0–9, A–Z	URL shorteners, compact IDs

Conversion Examples

Decimal	Binary	Octal	Hex
0	`0`	`0`	`0`
10	`1010`	`12`	`A`
42	`101010`	`52`	`2A`
127	`1111111`	`177`	`7F`
255	`11111111`	`377`	`FF`
1024	`10000000000`	`2000`	`400`
65535	`1111111111111111`	`177777`	`FFFF`

How Conversion Works

To decimal: Multiply each digit by its positional value (base^position) and sum them. E.g., binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10.
From decimal: Repeatedly divide by the target base and collect remainders. E.g., 255 ÷ 16 = 15 R 15, so hex = FF.
Between non-decimal bases: Convert to decimal first, then to the target base.

Prefix Conventions in Programming

0b — binary (e.g., 0b1010)
0o or 0 — octal (e.g., 0o755)
0x — hexadecimal (e.g., 0xFF)

Frequently Asked Questions

How do I convert decimal to binary?

Enter your decimal number in the converter — binary output appears instantly. For example, decimal 255 = binary 11111111. The tool also shows hex and octal simultaneously so you can compare all representations at once.

How do I convert hexadecimal to decimal?

Enter your hex value (with or without 0x prefix) and the tool converts it to decimal, binary, and octal instantly. For example, FF hex = 255 decimal. Useful for color codes, memory addresses, and bitwise operations.

What are the common number bases in programming?

Binary (base 2) — bit manipulation. Octal (base 8) — Unix file permissions. Decimal (base 10) — everyday numbers. Hexadecimal (base 16) — colors, memory addresses, and byte values.

How do I convert binary to hexadecimal?

Group binary digits in sets of 4 from the right, then convert each group to hex. 11111111 → 1111 1111 → FF. The converter does this automatically for any value you type.

What is hexadecimal used for in web development?

Hex represents CSS colors (#FF5733), HTML color codes, and byte values. Each hex color pair corresponds to a red, green, or blue channel from 00 (0) to FF (255).

Input

Results

Bit Visualization (32-bit)

Additional Info