Base Converter Calculator
Convert numbers between different bases (2-36)
Enter the number you want to convert
Type any valid number for the source base. For binary use only 0-1, for octal use 0-7, for decimal use 0-9, and for hexadecimal use 0-9 and A-F.
Select the source and target bases
Choose what base your number is in (From Base) and what base you want to convert to (To Base). Supports bases 2 through 36.
Click Convert to see the result
The converted number appears instantly. Copy it for use in programming, math homework, or digital systems work.
| Decimal | Binary (Base 2) | Octal (Base 8) | Hexadecimal (Base 16) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 255 | 11111111 | 377 | FF |
Note: Hexadecimal uses letters A-F to represent values 10-15. Base 36 uses all digits 0-9 and letters A-Z.
What Is a Number Base?
A number base tells you how many unique digits a system uses. Base 10 (decimal) uses ten digits: 0-9. Base 2 (binary) uses two: 0 and 1. Base 16 (hexadecimal) uses sixteen: 0-9 and A-F. The position of each digit represents a power of the base.
Binary (Base 2)
Binary is the language of computers. Every piece of data in your device is stored as ones and zeros. Each position represents a power of 2: 1, 2, 4, 8, 16, 32, and so on. The binary number 1011 equals 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal.
Octal (Base 8)
Octal was popular in early computing because it compresses binary nicely — each octal digit represents exactly three binary digits. It fell out of favor but still appears in Unix file permissions (like 755 or 644).
Hexadecimal (Base 16)
Hex is everywhere in computing. Memory addresses, color codes in CSS (#FF5733), and MAC addresses all use hex. Each hex digit represents four binary digits, making it compact and readable. FF in hex equals 255 in decimal.
Other Bases
Base 36 uses all 26 letters plus 10 digits, making it useful for short identifiers. Base 64 is used for encoding binary data in text formats. Base 12 (duodecimal) has advocates who argue it divides more cleanly than 10.
Know your valid digits
Each base has a maximum digit. Binary maxes at 1, octal at 7, decimal at 9, hex at F (15). Entering an invalid digit for the source base will cause errors.
Use hex for colors and memory
Web colors use six hex digits (RRGGBB). Memory addresses are often shown in hex. Learning to read hex quickly helps with debugging and web development.
Group binary for easier reading
Long binary strings are hard to read. Group them in fours (for hex) or threes (for octal). The binary 11010111 becomes D7 in hex or 327 in octal.
How do I convert binary to decimal?
Multiply each binary digit by its place value (powers of 2) and add them up. For 1011: (1×8) + (0×4) + (1×2) + (1×1) = 11. Start from the right with 2⁰=1, then 2¹=2, 2²=4, and so on.
Why does hexadecimal use letters?
Hex needs 16 unique symbols but only has 10 digits. Letters A through F represent values 10 through 15. So A=10, B=11, C=12, D=13, E=14, F=15. This keeps each hex digit as a single character.
What is base 36 used for?
Base 36 uses all 26 letters plus 10 digits, giving 36 unique symbols. It is useful for creating short, human-readable identifiers from large numbers. URL shorteners sometimes use base 36 or base 62.
How do programmers write different bases?
Many languages use prefixes: 0b for binary (0b1010), 0o for octal (0o17), and 0x for hex (0xFF). JavaScript, Python, and C all follow this convention. Decimal needs no prefix.
Can this calculator handle negative numbers?
This calculator works with positive integers. For negative numbers, convert the absolute value and add the minus sign. Note that computers use two's complement for negative binary numbers, which is more complex.
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