Binary, Hex, Decimal: How to Convert Between Number Bases

Why Number Base Conversion Matters

Computers think in binary (base 2). Humans prefer decimal (base 10). Programmers use hexadecimal (base 16) as a compact shorthand. If you work with low-level data, you need all three.

Common Number Bases

How Number Bases Work

Every number is a sum of digits × base^position. The rightmost digit is position 0.

Decimal Example: 423₁₀

4 × 10² = 4 × 100 = 400
2 × 10¹ = 2 × 10  =  20
3 × 10⁰ = 3 × 1   =   3
Sum: 423

Binary Example: 11010101₂

1 × 2⁷ = 128
1 × 2⁶ =  64
0 × 2⁵ =   0
1 × 2⁴ =  16
0 × 2³ =   0
1 × 2² =   4
0 × 2¹ =   0
1 × 2⁰ =   1
Sum: 213₁₀

Conversion Methods

Decimal to Binary (Repeated Division)

Divide by 2 repeatedly, reading remainders from bottom to top:

213 ÷ 2 = 106 remainder 1 ↑
106 ÷ 2 =  53 remainder 0 │
 53 ÷ 2 =  26 remainder 1 │
 26 ÷ 2 =  13 remainder 0 │
 13 ÷ 2 =   6 remainder 1 │
  6 ÷ 2 =   3 remainder 0 │
  3 ÷ 2 =   1 remainder 1 │
  1 ÷ 2 =   0 remainder 1 │
Result: 11010101₂

Binary to Hexadecimal (Grouping)

Group binary digits into sets of 4 (from right), then convert each group:

Binary:  1101 0101
Hex:       D    5
Result: 0xD5

Hexadecimal to Decimal

0xD5 = 13 × 16¹ + 5 × 16⁰
     = 208 + 5
     = 213₁₀

Using the ToolboxPro Converter

Visit our Number Base Converter and:

1. Type any number — it auto-detects the base

2. See all bases simultaneously — binary, octal, decimal, hex side by side

3. Copy any format with one click

4. Works with very large numbers — up to 64-bit values

Practical Use Cases

1. RGB Color Values

/* Hex is shorthand for RGB in base-10 */
#FF5733
/* FF = 255 red, 57 = 87 green, 33 = 51 blue */
background-color: rgb(255, 87, 51);

2. Unix File Permissions

# chmod uses octal
chmod 755 script.sh
# 7 = rwx (owner), 5 = r-x (group), 5 = r-x (others)
# 7 in octal = 111 in binary = read + write + execute

3. Bitwise Flags

// Each bit is a flag
const READ    = 0b0001;  // 1
const WRITE   = 0b0010;  // 2
const EXECUTE = 0b0100;  // 4

const permissions = READ | WRITE;  // 0b0011 = 3
const canRead = permissions & READ; // 0b0001 = true

4. Memory Addresses

// Debuggers show addresses in hex
int *ptr = malloc(64);
printf("%p", ptr);  // 0x7ffeefbff5e0

5. Network MAC Addresses

MAC: 00:1A:2B:3C:4D:5E
Each pair is one byte (0-255 in decimal, 00-FF in hex)
First 3 bytes: vendor ID, Last 3 bytes: device ID

Common Conversion Table

FAQ

What base do computers actually use? Binary (base 2). Every value in memory — numbers, text, images — is ultimately stored as sequences of 0s and 1s.

Why do programmers use hex? Hex is a human-readable shorthand for binary. One hex digit = 4 binary digits. It's much easier to read 0xFF than 0b11111111.

What about base64? Base64 uses 64 characters (A-Z, a-z, 0-9, +, /) and is used for encoding binary data as text — see our Base64 Encoder/Decoder.

Is there a base higher than hex? Yes — base32, base36, base58 (Bitcoin addresses), and base64 are common. Our tool handles bases 2 through 36.