Numbers Converter

Number systems represent values using different bases. Decimal (base 10) is everyday counting, while binary (base 2), octal (base 8) and hexadecimal (base 16) are used in computing and digital electronics.

This converter translates a number from any of these bases into all the others instantly.

Binary is how machines store numbers and it is unreadable at length. Hexadecimal exists because of an exact relationship: sixteen is two to the fourth, so one hex digit represents exactly four bits with no remainder. Any binary number splits into hex digits by grouping bits in fours, with no arithmetic required.

The number 255 is 11111111 in binary, 377 in octal and FF in hex. The hex form is two characters and maps directly onto the two four-bit halves of a byte, which is why memory addresses, colour codes and byte values are all written that way.

• A byte is eight bits, so exactly two hex digits: values 00 to FF.
• Octal groups three bits at a time and survives mainly in Unix file permissions, where three bits per permission set is exactly what is needed.
• Colour codes like #FF8800 are three bytes: red, green and blue, each 00 to FF.

A binary pattern does not carry its own interpretation. The eight bits 11111111 are 255 when read as an unsigned integer and −1 when read as a signed one, and nothing in the bits themselves says which is intended.

Signed values are normally stored in two's complement, where the top bit indicates sign and the negative values are formed by inverting and adding one. That gives an eight-bit signed range of −128 to 127 against an unsigned range of 0 to 255: the same 256 patterns, mapped to different numbers.

• This converter treats input as unsigned. Interpreting a stored value as signed requires knowing the width and the convention it was written with.
• Overflow is the practical consequence: adding 1 to the largest value in a fixed width wraps to the smallest rather than growing.
• Byte order matters once numbers span multiple bytes: the same value can be stored most significant byte first or last, which is why endianness has to be agreed between systems.