Value of a number written in base b
N = Σ d_i × b^i (i from 0 to n − 1)
Each digit is multiplied by the power of b of its place, the rightmost digit having place 0.
Number base converter: binary, octal, decimal, hex
Number base converter from 2 to 36: 255 = FF in hexadecimal = 11111111 in binary = 377 in octal. Positional notation, division method, #RRGGBB colours, chmod 755 permissions and bit masks.
- Clipboard
Number to convert
Results
Binary (base 2)
Octal (base 8)
Decimal (base 10)
Hexadecimal (base 16)
Target-base result
Was this tool useful?
How does this tool work?
Enter an integer in any base from 2 to 36 and read it at once in binary, octal, decimal and hexadecimal, plus the target base of your choice. Use it to decode a #RRGGBB colour, read Unix permissions like chmod 755, write a bit mask, check a number-systems exercise or handle base-36 identifiers.
In a positional system of base b, each digit is worth its place value, a power of b: 1F4 in base 16 equals 1 × 256 + 15 × 16 + 4 = 500. Bases above 10 use letters: A = 10, B = 11, up to F = 15 in hexadecimal and Z = 35 in base 36. Case is ignored when you type.
To go from decimal to base b, divide repeatedly by b and read the remainders from bottom to top: 500 = 31 × 16 + 4, then 31 = 1 × 16 + 15, so 1F4. Binary, octal and hexadecimal are linked because 8 = 2^3 and 16 = 2^4: one octal digit is 3 bits and one hex digit is 4 bits. So binary 1010 1010 groups into A and A, giving AA, or 170 in decimal.
Calculations use arbitrary-size integers: 18446744073709551615 (2^64 − 1) converts exactly to FFFFFFFFFFFFFFFF, which an ordinary JavaScript number cannot represent. The prefixes 0b, 0o and 0x are accepted for bases 2, 8 and 16, and spaces or underscores are ignored. A leading minus or plus sign is accepted.
Limits: only integers are handled, so fractional values such as 3.5 are rejected. A negative number is displayed with its sign (−42 gives −101010), not in two's complement, which depends on a chosen bit width. A digit that does not exist in the source base, such as 2 in binary, is reported.
How to use this tool
Enter the number and its base
Type the integer (with or without a 0x, 0b or 0o prefix) and pick the source base: 2, 8, 10, 16, 36 or a custom value from 2 to 36.
Pick the target base
Binary, octal, decimal and hexadecimal results are always shown, and the target base appears in its own field.
Adjust the display
Choose upper or lower case, and group digits by 4 (binary, hex) or 3 to make long values easier to read.
Positional notation and changing base
An integer N is written in base b with digits d_i between 0 and b − 1.
Euclidean division
N = q × b + r
The remainder r is the lowest digit in base b; repeat with q.
Binary grouping
16 = 2^4 and 8 = 2^3
One hex digit equals 4 bits and one octal digit 3 bits.
- N
- the integer to write
- b
- the base (2 to 36)
- d_i
- the digit at place i (0 to b − 1)
- q, r
- quotient and remainder of the division by b
Example: 500 ÷ 16 = 31 remainder 4; 31 ÷ 16 = 1 remainder 15 (F); 1 ÷ 16 = 0 remainder 1. Reading the remainders from bottom to top, 500 = 1F4 in hexadecimal.
Use cases
Web colours
Decode a #RRGGBB code into three decimal values from 0 to 255, or the other way round.
Unix permissions
Read an octal chmod mode as a sequence of r, w and x bits.
Bit masks and addresses
Write a bit mask, read a memory value or understand a binary field.
Computer science and maths classes
Check number-system exercises or compare the representations of one integer.
Examples
255 in hexadecimal
255 = 15 × 16 + 15, the largest value of one byte.
Input
255 (base 10)Result
FF in hexadecimal, 11111111 in binary, 377 in octalOrange CSS colour
FF = 255 (red), 88 = 136 (green), 00 = 0 (blue): rgb(255, 136, 0).
Input
FF8800 (base 16)Result
16746496 in decimalchmod 755
7 = 111 (rwx), 5 = 101 (r-x), 5 = 101 (r-x): rwxr-xr-x.
Input
755 (base 8)Result
111101101 in binary, 493 in decimalGrouped byte
Spaces are ignored, and each group of 4 bits gives one hex digit.
Input
1010 1010 (base 2)Result
AA in hexadecimal, 170 in decimalBase 36
1000 = 27 × 36 + 28, with R = 27 and S = 28.
Input
1000 (base 10)Result
RS in base 36Tips and best practices
- Quick link: 16 = 2^4, so one hex digit is exactly 4 bits (FF = 1111 1111).
- A byte has 8 bits: 00 to FF in hex, 0 to 255 in decimal.
- Bases above 16 use letters up to Z; input accepts upper and lower case.
- For numbers with a fractional part, convert the integer and fractional parts separately with a dedicated tool.
- Check a conversion by converting back: you should recover the starting number.
Sources and references
- Weisstein E.W., Base (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Binary (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Hexadecimal (opens in a new tab), Wolfram MathWorldPage in English
Frequently asked questions
How do I convert decimal to binary?
Divide by 2, note the remainders, and read them from bottom to top. For example 13 gives 1101: 13 = 6 × 2 + 1, 6 = 3 × 2 + 0, 3 = 1 × 2 + 1, 1 = 0 × 2 + 1.
How do I convert hexadecimal to decimal?
Multiply each digit by a power of 16. FF = 15 × 16 + 15 = 255, and 1F4 = 1 × 256 + 15 × 16 + 4 = 500.
Which bases are supported?
All integer bases from 2 to 36, including binary (2), octal (8), decimal (10), hexadecimal (16) and base 36 (digits 0-9 then A-Z).
Can I convert negative or fractional numbers?
Negatives are accepted with a minus sign and shown with their sign (−42 gives −101010), without two's complement. Fractional numbers are not accepted.
Is there a size limit?
Not in practice: the calculation uses arbitrary-size integers. 2^64 − 1 = 18446744073709551615 gives FFFFFFFFFFFFFFFF.
Related tools
Keep going with these tools
Tools similar or complementary to this one.
Similar tools
Convert a color between HEX, RGB, and HSL with equivalent values.
Mathematics & calculationUse this tool
Encode text as Base64 or decode a Base64 string back to its original content.
Mathematics & calculationFeaturedUse this tool
Write a number in words in English, French, Spanish, German, Italian or Portuguese, or turn written words back into digits.
Mathematics & calculationFeaturedUse this tool