Draft:Digital alphabet

This page is about alphabets in digital communications. For other uses, see Alphabet.

Digital alphabet is a term used in information theory, telecommunication, and computer science for any finite, discrete set of symbols chosen to represent information in a machine-readable form. Typical examples range from the binary alphabet {0, 1} that underpins modern electronics to large character repertoires such as Unicode. Digital alphabets make it possible to encode, transmit, store, and decode messages reliably because every symbol is unambiguously distinguishable from every other.

Definition and scope

A digital alphabet can be formalised as a finite alphabet $\Sigma =\{\sigma _{1},\sigma _{2},\ldots ,\sigma _{n}\}$ used by a discrete source.Claude Shannon’s 1948 paper defined a noiseless source as one that “chooses successively from a set of symbols” that constitute an alphabet.

Although the binary alphabet of two symbols is the simplest and today the most widespread, historical and contemporary systems employ alphabets of many sizes—for example the 5-bit Baudot code’s 32 symbols, ASCII’s original 128, or Unicode’s >149 000 characters.

Historical development

Early telegraphy

• Baudot code (1870 – 1874) replaced variable-length Morse symbols with fixed-length five-unit patterns, laying the groundwork for later digital codes.
• The Baudot family evolved into the International Telegraph Alphabet No. 2 (ITA 2) and remained in telex use until the 1960s.

ASCII and the early computer era

In 1963 the American Standards Association adopted ASCII, a 7-bit, 128-symbol digital alphabet designed for English-language data exchange between computers and peripherals. ASCII’s fixed length and simple parity bit made it attractive for early serial links, but it proved inadequate for multilingual computing.

Unicode and universal character sets

Unicode (first published 1991) provides a single digital alphabet intended to encode every writing system. As of version 16.0 it contains more than 149 000 characters across 168 scripts, plus numerous symbols and emojis. Variable-length UTF-8, UTF-16, and UTF-32 encodings preserve backward compatibility with ASCII while permitting much larger alphabets.

Theoretical properties

Alphabet size and information content

Shannon showed that the maximum information conveyed per symbol (entropy H) depends on both symbol probabilities and alphabet size. For a binary alphabet the maximum entropy is 1 bit per symbol; generalising to an n-ary alphabet yields $\log _{2}n$ bits per perfectly random symbol.

Binary alphabet

Research highlights the “curious case of the binary alphabet”: certain coding-theory and privacy results that hold for $n\geq 3$ take different forms when $n=2$.

Redundancy and error control

By adding check symbols from the same alphabet (parity bits, CRCs), a code can detect or correct errors introduced in a noisy channel, trading redundancy for reliability—an idea central to modern channel coding.

Applications

Domain	Role of the digital alphabet	Typical alphabet	Example
Telecommunications	Serial-line encoding, character framing	ASCII, ITA 2	Telex, RS-232
Data storage	Magneto-electric patterns for bytes	Binary 8-bit	SSD, HDD
Internet protocols	Packet payload text	UTF-8 (Unicode)	HTTP headers, JSON
Optical & radio links	Modulation symbols (QAM, PSK)	Binary, quaternary, 256-QAM symbols	Wi-Fi, LTE
Synthetic biology	Expanded DNA alphabets for data storage or biotechnology	A,C,G,T + artificial bases (e.g. P,Z)	Six-letter DNA aptamers

Relation to other concepts

• Alphabet in formal languages
• Character encoding
• Source coding and data compression
• Channel coding and error-correcting codes
• Barcode and QR code, visual digital alphabets

See also

• Baud
• Morse code
• Shannon–Fano coding
• Unicode Consortium