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Convert numbers across binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16) systems with Two's Complement signed integer encoding, bitwise bit shifts, and byte-level alignment.
B_s. Convert to decimal integer N_{10} = sum_{k=0}^{n-1} d_k cdot B_s^k where hex letters map: A=10, B=11, C=12, D=13, E=14, F=15.N_{10} to target radix B_t via integer division modulo: quotient q_{k} = lfloor N / B_t
floor, remainder r_k = N pmod{B_t}. Prepend remainder characters in reverse order.1101_1010_2). Map each nibble directly to one hex digit: 1101_2 = ext{D}_{16}, 1010_2 = ext{A}_{16} implies ext{DA}_{16}.k-bit registers: invert all bits (One's complement sim X) and add 1: ext{Two's Complement} = 2^k - |X|.Raw binary strings (e.g. 1101101011110001) are difficult for humans to read and prone to transcription errors. Hexadecimal compresses exactly 4 binary bits into a single character (0-9, A-F), meaning an 8-bit byte is always exactly 2 hex digits (e.g., 0xFF = 11111111) and a 32-bit memory address is exactly 8 hex characters.
Two's complement is the universal standard for signed integers in computer hardware because it allows addition and subtraction to use identical CPU circuitry without special handling for signs. To negate a number, flip all bits and add 1. In an 8-bit signed system, values range from -128 (10000000) to +127 (01111111), and zero has a single unique representation (00000000).
Group binary digits into blocks of 4 starting from the right (least significant bit). Add leading zeros to the leftmost block if needed. Replace each 4-bit nibble with its corresponding hex digit (0000=0 ... 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F).
Endianness determines how multi-byte numbers are ordered in computer memory. Big-Endian stores the most significant byte at the lowest memory address (natural reading order: 0x1234 -> [12, 34]). Little-Endian (standard in x86/x64 and ARM processors) stores the least significant byte first (0x1234 -> [34, 12]).