Binary, Hex & Decimal Converter
Convert instantly across binary, octal, decimal, and hexadecimal radices. Toggle individual register bits interactively.
Interactive Bit Register (16 Bits)
Click any individual bit to toggle between 0 and 1. MSB (Most Significant Bit) is on the left.
Computer Architecture & Positional Numeral Systems
Why Hexadecimal?
Computers fundamentally execute in binary (bits), but long binary strings like 11111111 are error-prone for humans to read.
Since 16 is exactly 2⁴, each hexadecimal digit cleanly maps to 4 binary bits (one nibble). An 8-bit byte maps to exactly two hex characters (e.g. 0xFF).
Two's Complement Negation
Modern CPUs represent negative integers using two's complement format: invert all bits and add 1.
This mathematical property eliminates the need for separate subtraction circuits in hardware, allowing addition and subtraction to share the exact same ALU logic.
Endianness & Word Sizes
A Byte is 8 bits (max 255), a Word is 16 bits (max 65,535), a Double Word (DWord) is 32 bits, and a Quad Word (QWord) is 64 bits.
In Little-Endian systems (like x86/ARM), the least significant byte is stored at the lowest memory address.