Number Base Converter
Every Base From 2 to 36, With Each Step Shown

Jobs This Number Base Converter Handles for You

This number base converter takes one number and writes it in every common base at once. Take 255: in binary it reads 11111111, in octal 377 and in hex FF. Type 0xFF instead, and the converter notices the prefix and reads it as hex without being told.

Numbers of any size go through fine. Most online converters quietly round anything above about sixteen digits, because they use ordinary floating-point numbers. This one uses exact whole-number maths, so a 40-digit ID or a 128-bit key comes out right to the very last digit.

Beyond the plain conversion, it shows what developers and students usually need next: the two’s complement form for signed integers, the number of bits and bytes, which integer types it fits, and the step-by-step working behind the answer.

How Number Bases Work

To begin with, a base is simply how many different digits a system uses. Base 10 relies on the ten digits 0 to 9. Base 2 gets by with only the digits 0 and 1. Hexadecimal has sixteen, so after 9 it borrows the letters A to F. Octal has eight, from 0 to 7.

In every base, each position is worth the base times the position to its right. Decimal places are worth 1, 10, 100, and upward from there. Binary place values run 1, 2, 4, 8, 16. So binary 1011 adds up as 8 + 0 + 2 + 1, giving 11 in decimal.

Binary to Decimal, Hex to Decimal and Back

The two conversions people search for most are binary to decimal and hex to decimal. Both work the same way here: type the number, pick the base it is written in, or let a 0b or 0x prefix decide, and every other base appears straight away.

For long binary numbers, the grouping switch splits the digits into blocks of four, which matches one hex digit each. That makes 1101 1110 1010 1101 far easier to check than a solid row of ones and zeros, and it shows at a glance that the hex form is DEAD.

Signed 8-, 16-, 32- and 64-Bit Values

Computers store negative whole numbers in a form called two’s complement. The highest bit acts as the sign, and the rest are flipped and shifted so that adding numbers still works. As a result, -1 in an 8-bit byte is 11111111, not 10000001.

The converter shows this form at 8, 16, 32 and 64 bits, in binary and hex. When a number is too big for a width, that row says so instead of showing a wrong pattern. For a deeper explanation, the two’s complement article on Wikipedia walks through the arithmetic.

Fractions, Exact to the Last Digit

Numbers with a point convert too. For example, 10.625 in decimal is exactly 1010.101 in binary. Some fractions, however, never end in another base. The decimal 0.1 becomes 0.000110011… in binary, repeating forever.

Instead of cutting such a number off without warning, the converter finds the repeating block and puts it in brackets: 0.0(0011). That is also the reason 0.1 + 0.2 is not exactly 0.3 in most programming languages, since the computer has to round that endless binary fraction somewhere.

Why Programmers Love Hexadecimal

Each hex digit covers exactly four bits, which is why a byte takes two of them. That is why colours are written as #FF8800, memory addresses as 0x7FFF, and file signatures as 89 50 4E 47. Hex is short enough to read and still maps cleanly to the bits underneath.

Hex to Decimal and Binary to Decimal in Daily Work

Web designers meet hex to decimal every day, because a colour such as #1B5FD1 is three hex bytes: 27, 95 and 209 for red, green and blue. Network staff, meanwhile, use binary to decimal when they read subnet masks, since 255.255.255.0 is simply twenty-four ones followed by eight zeros.

Programmers, in turn, read error codes, memory dumps and file headers in hex. So when a log says 0x80070005, typing it here shows the decimal value and the bit pattern at once. Likewise, students checking homework can compare their own working with the steps below.

Every Division and Multiplication Shown

Teachers, however, usually want the method, not only the answer. Open the working section, and the converter shows the classic repeated division: divide by the target base, write down the remainder, and carry on with the quotient. Write the remainders in reverse order, and those are the binary digits.

You can pick which base the working uses with the Also show menu. So the same page covers decimal to binary homework, decimal to hex and even base 7 exercises.

Base Conversion in Code

In fact, most languages can convert bases in one line. In JavaScript, parseInt("ff", 16) reads hex and (255).toString(2) writes binary. For numbers above 2 to the power of 53, however, use BigInt, or the last digits will be wrong.

Python has int("ff", 16) plus bin(), oct() and hex(). PHP offers base_convert(), which also loses precision on very large numbers. When you need a quick answer you can trust, this page is the easier check.