How Binary to Hexadecimal Conversion Works
Binary (base 2) uses only the digits 0 and 1. Hexadecimal (base 16) uses the digits 0 through 9 and the letters A through F, where A=10, B=11, C=12, D=13, E=14, and F=15. The key relationship is that 16 = 2 to the power of 4, which means one hexadecimal digit maps exactly to four binary digits (called a nibble).
To convert binary to hex, group the binary digits into sets of 4 starting from the rightmost digit. If the leftmost group has fewer than 4 digits, pad it with leading zeros. Then look up or calculate the hex value for each 4-bit group.
The 4-Bit Nibble Lookup Table
| Binary | Decimal | Hex | Binary | Decimal | Hex |
|---|
| 0000 | 0 | 0 | 1000 | 8 | 8 |
| 0001 | 1 | 1 | 1001 | 9 | 9 |
| 0010 | 2 | 2 | 1010 | 10 | A |
| 0011 | 3 | 3 | 1011 | 11 | B |
| 0100 | 4 | 4 | 1100 | 12 | C |
| 0101 | 5 | 5 | 1101 | 13 | D |
| 0110 | 6 | 6 | 1110 | 14 | E |
| 0111 | 7 | 7 | 1111 | 15 | F |
Worked Example
Convert binary 10101111 to hexadecimal:
- Split into nibbles from the right: 1010 | 1111
- Convert each nibble: 1010 = 10 = A, 1111 = 15 = F
- Concatenate: AF
So 10101111 in binary = AF in hexadecimal = 175 in decimal. You can verify: A (10) x 16 + F (15) = 160 + 15 = 175.
Why Use Hexadecimal?
Programmers and engineers use hexadecimal because it dramatically compresses binary representations. A full 8-bit byte such as 11001010 becomes just CA in hex. A 32-bit IPv4 address, a 24-bit RGB colour value, or a 64-bit memory address are all much more readable and writable in hex than in raw binary. Hexadecimal is also directly supported in most programming languages using the 0x prefix (for example, 0xAF in C, Python, or JavaScript evaluates to 175).
Hexadecimal in Common Contexts
- Colours in HTML and CSS: #RRGGBB format, such as #FF5733, where each pair of hex digits represents a colour channel from 00 (0) to FF (255).
- Memory addresses: Debuggers and disassemblers show addresses like 0x00400000.
- Network protocols: MAC addresses use six pairs of hex digits (e.g. 00:1A:2B:3C:4D:5E).
- File formats: Hex editors display raw file bytes as hex pairs, making it easy to inspect binary files without dealing with long binary strings.
Related Calculators
Method: Group binary digits into 4-bit nibbles from the right, padding with leading zeros as needed, then map each nibble to its hexadecimal digit using the standard nibble lookup table (0000=0 through 1111=F). This is equivalent to converting binary to decimal first, then to hexadecimal, but the nibble method is faster for manual conversion and is the basis for how computers internally represent data.
This converter handles unsigned binary integers of any length. It does not interpret two's complement negative numbers. For very large binary strings, the decimal equivalent shown uses JavaScript's standard number type, which is accurate to 53 bits. Strings longer than 53 bits will show an approximate decimal value, but the hexadecimal result remains exact because it uses nibble-by-nibble string conversion.
