A number base converter online instantly translates any number between decimal, binary, octal, and hexadecimal - the four number systems every developer encounters regularly.
What are Number Bases?
A number base (or radix) is the number of unique digits a positional numeral system uses. The most common bases in computing are:
- Base 10 (Decimal) - digits 0–9, the system humans use every day
- Base 2 (Binary) - digits 0 and 1, the native language of computers
- Base 8 (Octal) - digits 0–7, used in Unix file permissions and some legacy systems
- Base 16 (Hexadecimal) - digits 0–9 and A–F, used for memory addresses, colors, and byte representations
How to Use the Base Converter
- Open the Number Base Converter on UtilWave.
- Type a value in any of the four fields (decimal, binary, octal, or hex).
- All other fields update instantly with the converted values.
- There is no conversion button - results appear as you type.
- Copy the value in any base with one click.
Conversion Examples
| Decimal | Binary | Octal | Hexadecimal | |---|---|---|---| | 0 | 0 | 0 | 0 | | 10 | 1010 | 12 | A | | 16 | 10000 | 20 | 10 | | 255 | 11111111 | 377 | FF | | 256 | 100000000 | 400 | 100 | | 1024 | 10000000000 | 2000 | 400 |
When Developers Need Base Conversion
Colors in CSS and design - #FF5733 is hex for RGB (255, 87, 51). Designers and developers switch between decimal RGB and hex constantly.
Memory addresses - Debuggers, disassemblers, and hardware documentation display memory addresses in hexadecimal.
Bitmask operations - Understanding 0xFF, 0x0F, or 0b11110000 requires quick decimal-to-hex/binary lookups.
Unix file permissions - chmod 755 uses octal. Permission 0755 = binary 111 101 101 = read/write/execute for owner, read/execute for group and others.
Network subnetting - Subnet masks like 255.255.255.0 are easier to understand when seen as 11111111.11111111.11111111.00000000 in binary.
Assembly and embedded programming - CPU registers and hardware registers are almost always documented in hexadecimal.
FAQ
Can I convert negative numbers? The tool handles non-negative integers. Negative numbers in computing use two's complement representation, which varies by word size.
Is there a size limit on the numbers I can convert? The tool handles numbers up to JavaScript's safe integer range (2^53 - 1). For cryptographic or 64-bit values, use a specialized bignum tool.
What is the difference between 0x10 and 10 in hex?
0x is just a prefix convention in code (C, JavaScript, Python) indicating that the following digits are hexadecimal. In the converter, enter just 10 in the hex field without the 0x prefix.
Why do computers use binary and hex instead of decimal? Binary maps directly to the two physical states of digital circuits (on/off). Hexadecimal provides a compact, human-readable way to express binary - each hex digit represents exactly four binary digits (bits).
Convert any number in seconds with the free Number Base Converter.