Computers use binary (base 2) internally. Programmers often work with hexadecimal (base 16). Understanding these systems demystifies how computers store and display data.
The Three Systems
| System | Base | Digits Used | |--------|------|-------------| | Binary | 2 | 0, 1 | | Decimal | 10 | 0–9 | | Hexadecimal | 16 | 0–9, A–F |
In hex: A=10, B=11, C=12, D=13, E=14, F=15
Binary to Decimal
Each binary digit represents a power of 2, starting from the right.
Example: Convert 1101 (binary) to decimal
1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 8 + 4 + 0 + 1
= 13
Decimal to Binary
Divide repeatedly by 2, recording remainders:
Example: Convert 25 to binary
25 ÷ 2 = 12 remainder 1
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Read remainders bottom to top: 11001
Check: 16 + 8 + 0 + 0 + 1 = 25 ✓
Hexadecimal to Decimal
Each hex digit represents a power of 16:
Example: Convert 2F (hex) to decimal
2×16¹ + F×16⁰
= 2×16 + 15×1
= 32 + 15
= 47
Binary to Hexadecimal (Quick Method)
Group binary digits in sets of 4 from the right, convert each group:
Example: 11010111 binary to hex
1101 = 13 = D
0111 = 7
Result: D7 hex
Why Hex?
8 binary digits (a byte) = exactly 2 hex digits. So:
- 00000000 = 00 (hex) = 0
- 11111111 = FF (hex) = 255
This makes hex a compact way to represent binary data. Web colors use hex (e.g., #FF5733 = red 255, green 87, blue 51).
Common Values
| Decimal | Binary | Hex | |---------|--------|-----| | 0 | 0000 | 0 | | 10 | 1010 | A | | 15 | 1111 | F | | 16 | 10000 | 10 | | 255 | 11111111 | FF | | 256 | 100000000 | 100 |
Use our Number Base Converter to convert between binary, decimal, hexadecimal, and octal instantly.