Number Base Converter
Convert numbers between decimal, binary, octal, and hexadecimal in your browser.
Click any value to copy
What it's for
Conversion between numeral systems
All bases at once
Type a number and instantly see its equivalent in decimal, binary, octal, and hexadecimal simultaneously.
100% private
Conversion happens in your browser using pure JavaScript. No data is sent to any server.
Large integers
Supports large integers, useful for debugging memory addresses and network calculations.
Instant
Results appear as you type, no buttons or waiting required.
How it works
Three steps, no hassle
Enter the source number
Type the number you want to convert and select its source base: decimal (base 10), binary (base 2), octal (base 8), or hexadecimal (base 16).
View all base equivalents
The converter automatically displays the equivalent in all bases simultaneously. No need to select them one by one.
Copy the result
Click any result field to copy the value to your clipboard with a single click.
FAQ
Got questions?
A number base (or positional numeral system) defines how many distinct symbols are used to represent quantities. Base 10 (decimal) uses digits 0-9 as we use daily. Base 2 (binary) uses only 0 and 1. Base 8 (octal) uses 0-7. Base 16 (hexadecimal) uses 0-9 and A-F. The value of each digit depends on its position multiplied by the corresponding power of the base.
Digital electronic circuits work with two stable physical states: high voltage (1) and low voltage (0). This direct correspondence between physical states and binary digits makes binary the natural language of hardware. Gottfried Wilhelm Leibniz formulated the binary system in 1679 and anticipated its potential for mechanical computation, though he could not foresee its application in electronics three centuries later.
Hexadecimal is a compact representation of binary: each hex digit equals exactly 4 bits. It is widely used in CSS colors (#FF5733 is orange-red), network MAC addresses (00:1A:2B:3C:4D:5E), system error codes, memory debugging, and assembly instructions. It is more readable than raw binary while maintaining direct correspondence with bits.
Octal was common in early computers of the 1960s-70s (PDP-8, CDC 6000). Today its main use is in Unix/Linux file permissions: the chmod 755 command uses octal, where 7=rwx (read+write+execute), 5=r-x (read+execute), representing permissions for owner, group, and others respectively.
Use the successive division method: divide the number by 2 and note the remainder (0 or 1). Divide the quotient by 2 again. Repeat until the quotient is 0. Read the remainders from bottom to top. Example: 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1 → 1101 in binary. Verify: 1×8 + 1×4 + 0×2 + 1×1 = 13.
Number systems: history of binary, octal, and hexadecimal
Positional numeral systems have a millennia-long history. The Babylonians used base 60 (sexagesimal) over 4,000 years ago, a legacy that persists today in the 60 minutes of an hour and 360 degrees of a circle. The Hindu-Arabic decimal system, with the revolutionary concept of zero, reached Europe in the 10th century through Al-Khwarizmi and Fibonacci, displacing Roman numerals.
The binary system was formalized by Gottfried Wilhelm Leibniz in 1679, who saw in it a pure representation of logic (being and non-being). George Boole expanded this vision with Boolean algebra in 1854. Claude Shannon demonstrated in 1937 that electrical circuits could implement Boolean algebra, laying the foundations of modern digital electronics. The first electronic digital computer (ENIAC, 1945) operated internally in binary.
Hexadecimal became popular with the first microprocessors of the 1970s. The Intel 8080 and Motorola 6800 used 8-bit words, perfectly represented by two hexadecimal digits. Modern development tools display memory dumps in hex, debuggers use hex addresses, and web colors in CSS have used hexadecimal notation since the HTML 3.2 specification of 1997.