Number Base Converter (Binary, Decimal, Octal, Hex)
Convert a number between binary, octal, decimal and hexadecimal. Enter a value and choose its base.
Use valid digits for the chosen base (e.g. only 0 and 1 for binary).
What Is a Number Base Converter?
A number base converter changes a number from one numeral system to another. The four most common bases are binary (base 2), octal (base 8), decimal (base 10) and hexadecimal (base 16). Decimal is the system humans use every day with digits 0 to 9, while binary, octal and hexadecimal are the languages of computing and programming.
The base, also called the radix, is simply how many different digit symbols the system uses. Binary uses only 0 and 1, octal uses 0 to 7, decimal uses 0 to 9, and hexadecimal uses 0 to 9 followed by the letters A to F to stand for the values ten to fifteen. This tool converts any whole number between all four bases instantly.
How It Works: Place Value and Conversion
Every numeral system uses place value, where each position is worth a power of the base. In decimal, the number 253 means 2 hundreds, 5 tens and 3 ones. In binary, each place is a power of two, in octal a power of eight, and in hexadecimal a power of sixteen.
To convert by hand, two methods cover everything:
- From any base to decimal (weighted sums): multiply each digit by its place value, then add the results. For binary 1010, that is (1×8) + (0×4) + (1×2) + (0×1) = 10.
- From decimal to any base (repeated division): divide the number by the target base, write down the remainder, and repeat with the quotient until it reaches zero. Reading the remainders from bottom to top gives the answer.
Worked Example
Take the binary number 1010 and convert it across all four bases.
Binary to decimal: using weighted sums, (1×8) + (0×4) + (1×2) + (0×1) = 8 + 0 + 2 + 0 = 10.
Decimal to octal: divide 10 by 8 to get 1 remainder 2, then divide 1 by 8 to get 0 remainder 1. Reading remainders bottom to top gives 12 in octal.
Decimal to hexadecimal: 10 in hexadecimal is the single digit A, because A stands for ten. So binary 1010 equals decimal 10 equals octal 12 equals hex A.
Where Number Bases Are Used
Different bases dominate different parts of computing because they map neatly onto how machines store data.
- Binary is the native language of computers, since every transistor is either off (0) or on (1). All data, from text to images, is ultimately stored in binary.
- Hexadecimal is a compact shorthand for binary, where each hex digit represents exactly four binary digits. It is widely used for memory addresses, colour codes such as web colours like FF0000 for red, and debugging.
- Octal groups binary into threes and appears in file permission settings on Unix and Linux systems.
- Decimal remains the system people read and write, so converters bridge the gap between human-friendly and machine-friendly numbers.
Understanding base conversion is a core skill for programmers, network engineers and anyone studying computer science.
Frequently Asked Questions
Multiply each binary digit by its place value, which is a power of two, then add the results. For binary 1010, the calculation is (1×8) + (0×4) + (1×2) + (0×1) = 10. The rightmost digit is the ones place, and each place to the left doubles in value.
Use repeated division by two. Divide the number by 2, record the remainder, then divide the quotient by 2 and repeat until you reach zero. Reading the remainders from bottom to top gives the binary number. For example, 10 divided this way gives 1010.
Hexadecimal uses sixteen digit symbols, but there are only ten numeric digits, so the letters A to F represent the values ten to fifteen. A is 10, B is 11, C is 12, D is 13, E is 14 and F is 15. This keeps every hex digit a single character.
Computers are built from transistors that have two stable states, off and on, which map naturally to 0 and 1. Representing data with just two symbols makes the electronics simpler and more reliable, so binary became the foundation of all digital computing.
Octal, base 8, groups binary digits into sets of three, which makes it a tidy shorthand for binary. Its most common modern use is in Unix and Linux file permissions, where values such as 755 describe read, write and execute rights for different users.
Yes. The number base converter handles binary, octal, decimal and hexadecimal in any direction. You can convert hex to binary, decimal to octal, or any other combination, and it works through decimal internally to give an accurate result.