Binary, Decimal, Hexadecimal and Octal Converter

How positional number systems work

In base b, each digit has a place value that is a power of b. The decimal number 175 means 1·10² + 7·10¹ + 5·10⁰. The same value in binary (base 2) is 10101111, which means 1·2⁷ + 0·2⁶ + 1·2⁵ + 0·2⁴ + 1·2³ + 1·2² + 1·2¹ + 1·2⁰. Computers use binary because each digit maps to a two-state circuit, and use octal and hexadecimal as compact ways to write binary.

Converting decimal to another base

Divide the number by the target base, write down the remainder, and repeat with the quotient until it reaches 0. The remainders, read from last to first, are the digits. For 175 in base 2 the remainders are 1, 1, 1, 1, 0, 1, 0, 1 from the first division to the last, giving 10101111 when read in reverse.

Why hexadecimal and octal are convenient

Since 16 = 2⁴, each hexadecimal digit equals exactly four binary digits (a nibble), and two hexadecimal digits make a byte. So 10101111 splits into 1010 and 1111, which is AF in hexadecimal. Octal works the same way with groups of three bits, because 8 = 2³.

Using the converter

Type in any field and the other fields update at once. Prefixes 0b, 0o and 0x are accepted, as are a leading minus sign and spaces. The details panel shows the bit length, the binary and hexadecimal values grouped for easy reading, and how many bytes are needed. The custom-base field handles every base from 2 to 36, using the letters A to Z for digits above 9.

Negative numbers are shown with a minus sign rather than in two's complement, so −5 becomes −101 in binary. Two's complement depends on a chosen word size (8, 16, 32 bits), which is a separate topic in computer architecture. Fractions are not converted here: the tool works with integers only, which keeps every result exact.