Data Representation Computer Science

A computer never actually stores a number, a letter, or a picture — it stores voltage levels that are either high or low, and every single thing a program manipulates is ultimately a human-chosen interpretation layered on top of that one physical fact. A bit is the smallest unit of that information, a single binary digit that is either 0 or 1, corresponding directly to one transistor's low or high state on the actual silicon this site covers at the device level. A byte groups eight bits together, giving 256 distinct patterns (2 to the 8th power), which is why a single byte is the natural unit for representing one character of text or one small number. Binary notation writes numbers using only the digits 0 and 1, with each position worth a power of two — the binary number `1011` means one eight, zero fours, one two, one one, adding up to eleven in ordinary decimal. Hexadecimal, base 16, exists purely as a convenience for humans reading binary: each hex digit (0 through 9, then A through F) represents exactly four bits, so a full byte fits neatly into two hex digits, which is why memory addresses, color codes, and MAC addresses are almost always written in hex rather than binary or decimal — it is simply more compact and easier for a person to transcribe without error. Text encoding is the agreed-upon mapping from bit patterns to characters: ASCII, the oldest and simplest widely used scheme, assigns the capital letter A to decimal 65 (binary `01000001`) and covers the basic English alphabet, digits, and punctuation in just seven bits; Unicode and its common encoding UTF-8 extend this same idea to represent essentially every writing system and symbol in use anywhere, using a variable number of bytes per character so that ASCII text happens to already be valid UTF-8, a deliberate backward-compatibility design choice. Integers are stored as fixed-width binary numbers — a 32-bit signed integer can represent roughly plus or minus two billion, with one bit conventionally reserved to indicate the sign using a scheme called two's complement, which is why integer values wrap around unexpectedly to a large negative number if a program adds past the maximum representable value, a real and common source of bugs. Floating-point numbers represent values with a fractional part by storing a sign bit, an exponent, and a mantissa (significant digits) separately, following the IEEE 754 standard nearly every modern CPU and programming language uses — this is also why `0.1 + 0.2` famously does not equal exactly `0.3` in most programming languages, because many decimal fractions simply cannot be represented exactly in binary, the same way one-third cannot be written exactly as a finite decimal.

Every data structure and algorithm this series covers next is built on these representations without exception — a linked list's pointer is just an integer holding a memory address, a string is just a sequence of bytes under one of these text encodings, and understanding why that integer can overflow or why that float can lose precision is what separates debugging a program from guessing at it.