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Binary, Hex, and Octal: The Number Base Cheat Sheet Every Developer Needs

#productivity #beginners #tools #webdev

If you've spent any time reading through assembly output, CSS colour values, UNIX permissions, or network documentation, you've run into number bases. Most developers get by just knowing that 0xFF means 255 — but understanding why unlocks a lot of the magic that happens at the hardware and protocol levels.

This is a short reference. Keep it bookmarked.

The four number systems you actually need

Decimal (base 10)

The one you grew up with. Ten digits: 0 through 9.

Every digit position represents a power of 10:

342 = 3×10² + 4×10¹ + 2×10⁰
    = 300 + 40 + 2
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Nothing surprising here.

Binary (base 2)

Two digits: 0 and 1. Every digit position represents a power of 2.

1011 (binary) = 1×2³ + 0×2² + 1×2¹ + 1×2⁰
              = 8 + 0 + 2 + 1
              = 11 (decimal)
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Where you'll see it:

  • Bitwise operations (&, |, ^, <<, >>)
  • Network masks (/24 = 11111111.11111111.11111111.00000000)
  • Flags and permissions (chmod 755 — more on this below)
  • Low-level debugging, registers, microcontrollers

Quick rule: the highest value of an n-bit number is 2ⁿ - 1. An 8-bit byte tops out at 255.

Hexadecimal (base 16)

Sixteen digits: 0–9, then A–F (where A=10, B=11, ..., F=15). Each hex digit represents exactly 4 binary bits, which makes hex a compact shorthand for binary.

0xFF = 1111 1111 (binary) = 255 (decimal)
0x1A = 0001 1010 (binary) = 26 (decimal)
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Where you'll see it:

  • HTML/CSS colours: #2F855A = R:0x2F G:0x85 B:0x5A
  • Memory addresses: 0x7fff5fbff8b0
  • SHA-256 and MD5 hashes: 5d41402abc4b2a76b9719d911017c592
  • UTF-8 escape sequences: A = "A"
  • MAC addresses: 00:1A:2B:3C:4D:5E
  • File headers (magic bytes): 89 50 4E 47 = PNG

One hex digit = 4 bits = one nibble. Two hex digits = 1 byte = 8 bits. This is why hex values always appear in pairs in memory dumps.

Octal (base 8)

Eight digits: 0 through 7. Less common today, but you encounter it every time you use chmod.

chmod 755 myfile
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That 755 is octal:

7 = 111 binary = read(4) + write(2) + execute(1) → owner: full access
5 = 101 binary = read(4) + execute(1)            → group: read + execute
5 = 101 binary = read(4) + execute(1)            → others: read + execute
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Each octal digit maps directly to 3 binary bits — which is why it was popular on 12-bit and 36-bit machines before 16-bit architectures made hex the standard.

In code, octal literals are prefixed with 0 in C/C++/JavaScript:

console.log(0755); // 493 in decimal (legacy syntax)
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Conversion cheat sheet

Decimal Binary Octal Hex
0 0000 0 0
8 0000 1000 10 8
10 0000 1010 12 A
15 0000 1111 17 F
16 0001 0000 20 10
32 0010 0000 40 20
64 0100 0000 100 40
127 0111 1111 177 7F
128 1000 0000 200 80
255 1111 1111 377 FF

Mental shortcuts that actually stick

Hex to decimal fast: Split into two nibbles, multiply the left by 16, add the right.

0xB4 = 11×16 + 4 = 176 + 4 = 180

Is a hex colour light or dark? If both R, G, B values are above 0x88 (136), it's a light colour. Below 0x44 (68) is very dark.

Binary shifts = powers of 2:

n << 1 doubles n. n >> 1 halves it (integer).

Useful for performance tricks and flags.

Octal digits = 3 bits each, Hex digits = 4 bits each. This is why UNIX permissions use three octal digits (3 actors × 3 permission bits = 9 bits total).

Converting quickly in the browser

If you need to convert between bases without pulling up a terminal, a free browser-based tool does all four at once:

Number Base Converter — snappytools.app

Type in any field (binary, octal, decimal, or hex) and all others update live. Handles arbitrary-precision integers using JavaScript's BigInt, so SHA-256 hash values won't overflow.

In JavaScript 

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

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

// Hex literals
0xFF    // 255
0o377   // 255 (modern octal syntax — note lowercase 'o')
0b11111111 // 255 (binary literal — ES2015+)
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Number bases are one of those fundamentals that pay dividends every time you read a stack trace, configure a firewall rule, or decode a protocol. Fifteen minutes with the conversion table above and it clicks permanently.

SnappyTools builds free, fast, browser-based tools for developers and designers. No signup, no data uploaded.

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