Information Encoding and Binary Representation

Everything Is Bits

A computer stores and processes information using just two states — on and off, high and low voltage — represented by the digits 0 and 1. A single such digit is a bit (binary digit); eight bits make a byte. Everything a computer holds — numbers, text, images, sound, instructions — is ultimately a pattern of bits. What a pattern means depends entirely on how it is interpreted.

Numbers are stored in binary (base 2), where each position is a power of 2 rather than a power of 10. Reading right to left, the positions are worth $1, 2, 4, 8, 16, \dots$. The binary number $1011$ therefore equals $8 + 0 + 2 + 1 = 11$ in decimal.

An 8-bit byte can represent $2^8 = 256$ distinct values, from $0$ to $255$. In general, $n$ bits give $2^n$ combinations. Because long binary strings are hard to read, programmers use hexadecimal (base 16, digits $0$–$9$ then $A$–$F$), where each hex digit packs exactly 4 bits — so one byte is exactly two hex digits.

Text is encoded by mapping characters to numbers: ASCII uses 7 bits per character (128 symbols), while Unicode extends this to cover every writing system.

Common pitfall: thinking a bit pattern has an inherent meaning. The same byte $01000001$ is the number $65$, the letter $A$ in ASCII, or part of a color — the interpretation, not the bits, decides. Always ask how a pattern is being read before deciding what it represents.

An 8-cell binary ruler: each cell labelled with its power of 2 (128 down to 1). A sample byte lights its set bits in accent, and the lit place values drop one by one into a running sum beneath.

$$d = \sum_{i=0}^{n-1} b_i \cdot 2^i$$