Number System Converter - Binary, Octal, Decimal, Hex
Number Systems in Computing
Computers use different number bases for different purposes. Binary (base 2) is the native language of all digital hardware. Octal (base 8) and hexadecimal (base 16) provide compact representations of binary data. Decimal (base 10) is what humans naturally use. Understanding these conversions is essential for programmers, CS students, and electronics engineers.
Quick Reference: Common Values
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 10 | 1010 | 12 | A |
| 16 | 10000 | 20 | 10 |
| 64 | 1000000 | 100 | 40 |
| 127 | 1111111 | 177 | 7F |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
Frequently Asked Questions
What is decimal 255 in binary?
Decimal 255 in binary is 11111111. It is also FF in hexadecimal and 377 in octal. 255 is significant in computing as the maximum value of an 8-bit unsigned integer, and is used in IPv4 subnet masks.
How do I convert binary to decimal?
To convert binary to decimal, multiply each bit by its positional power of 2 and sum them. For example: 1011 in binary = 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11 in decimal.
What is hexadecimal used for?
Hexadecimal (base 16) is widely used in computing for memory addresses, colour codes (e.g. #FF5733 in HTML/CSS), and representing binary data in a compact human-readable form. Each hex digit represents exactly 4 binary bits.
What digits are used in hexadecimal?
Hexadecimal uses the digits 0-9 and the letters A-F, where A=10, B=11, C=12, D=13, E=14, F=15. Both uppercase and lowercase letters are valid.
Why is octal (base 8) used in computing?
Octal was historically used in older computing systems and is still used in Unix/Linux file permissions (e.g. chmod 755). Each octal digit represents exactly 3 binary bits, making it a compact way to express binary data.
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