How to Convert Numbers Between Decimal, Binary, Hex & Octal

The Four Number Bases

Base	Name	Digits	255 in this base	Used for
Base 10	Decimal	0–9	255	Everyday numbers
Base 2	Binary	0, 1	11111111	CPU instructions, bitwise ops
Base 16	Hexadecimal	0–9, A–F	FF	Colors, memory addresses, hashes
Base 8	Octal	0–7	377	Unix file permissions (chmod 755)

Quick Reference Table (0–15)

Dec	Bin	Hex	Oct	Dec	Bin	Hex	Oct
0	0000	0	0	8	1000	8	10
1	0001	1	1	9	1001	9	11
2	0010	2	2	10	1010	A	12
3	0011	3	3	11	1011	B	13
4	0100	4	4	12	1100	C	14
5	0101	5	5	13	1101	D	15
6	0110	6	6	14	1110	E	16
7	0111	7	7	15	1111	F	17

Converting in Code

JavaScript

// Decimal → other bases
(255).toString(2);   // "11111111" (binary)
(255).toString(16);  // "ff" (hex)
(255).toString(8);   // "377" (octal)

// Other bases → decimal
parseInt("11111111", 2);  // 255
parseInt("ff", 16);        // 255
parseInt("377", 8);        // 255

// Hex literals in JS
const color = 0xFF5733;   // decimal 16733987
const byte  = 0b10110011; // binary literal = 179
const perm  = 0o755;      // octal literal = 493

Python

n = 255
bin(n)   # '0b11111111'
hex(n)   # '0xff'
oct(n)   # '0o377'

# Literals
b = 0b11111111  # binary → 255
h = 0xFF        # hex → 255
o = 0o377       # octal → 255

# String to int
int('ff', 16)       # 255
int('11111111', 2)  # 255

Practical Uses

CSS Colors (Hex)

#FF5733 = R:255, G:87, B:51. Each pair of hex digits represents one byte (0–255) of a color channel. #RGB shorthand: #F53 = #FF5533.

Unix Permissions (Octal)

chmod 755 = 111 101 101 in binary = rwx r-x r-x. Owner: 7=rwx, Group: 5=r-x, Other: 5=r-x.

Bitwise Operations

IP subnet masks, feature flags, and bitmasks are often expressed in binary or hex. 0xFF = 0b11111111 = all 8 bits set.

Memory Addresses

Debuggers and assembly use hex addresses: 0x7fff5fbff8a0. More compact than binary and easier to read than decimal for large numbers.

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