Base Converter

1. Choose the input base: decimal, binary, octal or hex.
2. Enter the value in that base.
3. Read the decimal result.
4. See the binary and hexadecimal forms too.

Here is what each result means:

A number base, or radix, is how many digits a counting system uses and what each place is worth. We normally count in base 10, decimal, with ten digits from 0 to 9, where each place to the left is worth ten times the one before. Computers, though, use other bases that suit how they store and process data.

Binary, base 2, uses only 0 and 1, matching the on-off states of electronic switches, so it is the native language of computers. Hexadecimal, base 16, uses 0 to 9 and then A to F for the values ten to fifteen; it is a compact way to write binary, since each hex digit stands for exactly four binary digits. Octal, base 8, uses 0 to 7 and appears in some older systems.

All of these are positional systems, so the same idea applies to each: the rightmost place is worth 1, and each place to the left multiplies by the base. Converting between them does not change the number itself, only how it is written. The decimal 255, the binary 11111111 and the hex FF are all the same value.

It reads your value in the chosen base and rewrites it in the others.

1. Your value is checked to make sure every digit is valid for the input base.
2. It is read into an ordinary decimal number.
3. That number is rewritten in binary, octal, decimal and hexadecimal.

For other number tools, see the Roman numeral converter and the scientific notation calculator.

Convert the decimal number 255.

Result: 255 is 11111111 in binary (eight ones), 377 in octal, and FF in hexadecimal. FF is compact because each F stands for four binary ones.

Each base uses a different set of digits.

Binary and hexadecimal pair up neatly: one hex digit equals exactly four binary digits, so hex is a short, readable way to write long binary strings. This is why hexadecimal is common in programming and colour codes.

The same value is written very differently in each base.

Higher bases pack the same value into fewer digits. That is why hexadecimal is popular for writing memory addresses and byte values, where a compact form is easier to read than a long row of ones and zeros.

The Input Base

The same digits mean different values in different bases, so choosing the right input base is essential.

Valid Digits

Each base allows only certain digits; a 2 is not valid in binary, and a G is not valid in hex.

The Size of the Number

Very large numbers can lose exactness once they pass the safe integer limit.

Programming

Convert between decimal, binary and hex when working with code or data.

Networking and Colours

Read hex colour codes or byte values in different bases.

Learning

See how the same number looks across counting systems.

1. Wrong Input Base

10 in binary is 2 in decimal, not ten. Always set the base you are entering.

2. Invalid Digits

Binary uses only 0 and 1; hex goes up to F. Other characters are not valid.

3. Confusing Hex Letters

In hex, A to F are digits for 10 to 15, not letters of a word.

4. Dropping Leading Zeros

Leading zeros do not change the value, but keep byte widths in mind when they matter.

5. Very Large Numbers

Beyond the safe integer limit, conversions may lose exactness.

Conversions are exact for non-negative whole numbers within the safe integer range.

Repeatedly divide by 2 and read the remainders from bottom to top. This converter does it for you: 255 in decimal is 11111111 in binary.

255 is FF in hexadecimal. Each F stands for 15, and the value is 15 times 16 plus 15, which is 255.

Hexadecimal uses 0 to 9 and then A, B, C, D, E and F for the values 10 to 15, giving sixteen digits in all.

Binary matches the on-off states of electronic switches, so 0 and 1 map directly to off and on. Everything a computer stores is built from these two digits.

Both are used in computing, but binary uses two digits and hex sixteen. One hex digit equals exactly four binary digits, so hex is a shorter way to write binary.

This tool converts between decimal, binary, octal and hexadecimal, the four most common bases. Choose which base you are entering from the toggle.

No. It converts non-negative whole numbers only. Negative numbers and fractions are outside its range.

Octal, base 8, groups binary digits in threes. It was common in older computer systems and still appears in some settings, such as file permissions.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Radix (number base) (Wikipedia).
• Binary number (Wikipedia).
• Hexadecimal (Wikipedia).