Skip to content

Units of Information

Choose a logarithmic reference base and unit convention for information quantities so the same amount can be expressed coherently in bits or shannons, nats, hartleys, and their standardized multiples without confusing information with storage capacity.

Version
v3 · 2026-09-06 · History
Domain-specific #
3036
Origin domain
information science
Subdomain
information theory
Aliases
Units of information and data, Information units

Core Idea

Units of information are reference units used to express logarithmic information quantities and closely related data quantities. If an information measure is written with logarithm base \(b\), changing the base rescales every value by a constant: \(\log_c x=\log_b x/\log_b c\). Shannon made the principle explicit: the choice of logarithmic base corresponds to the choice of a unit. Base two yields the bit or, under standards that distinguish the information-theoretic unit name, the shannon; base \(e\) yields the nat; and base ten yields the hartley.

Scope of Application

The unit family is literal in information theory, coding, data storage, communication engineering, and software measurement when quantitative claims must be compared or converted.

  • Source coding. Reporting entropy and average code length in base-two units.
  • Channel analysis. Expressing capacities per symbol or per second with a named logarithmic base.
  • Data storage. Distinguishing bit and byte capacities from statistical information content.
  • File and memory reporting. Applying decimal or binary prefixes without ambiguity.
  • Cryptography. Expressing key-space or uncertainty measures while preserving probability assumptions.
  • Software metrology. Relating data quantities to units and declared measurement procedures.

Clarity

Name the quantity first, then give its mathematical definition, logarithm base, unit name, symbol, and any rate denominator. State whether 'bit' means binary digit, storage capacity, or base-two information unit, and use 'shannon' when the governing standard or audience requires that distinction. Write conversions explicitly: one nat equals \(\log_2 e\) base-two units and one hartley equals \(\log_2 10\) base-two units. For bytes and prefixes, state that \(1\,\mathrm B=8\,\mathrm{bit}\), \(1\,\mathrm{kbit}=10^3\,\mathrm{bit}\), and \(1\,\mathrm{Kibit}=2^{10}\,\mathrm{bit}\).

Manages Complexity

The unit system allows results derived with different logarithmic bases or engineering conventions to be compared by multiplication rather than re-derivation. It separates the invariant information relation from a conventional numeric scale: changing from bits to nats changes the number but not the underlying ordering or coding conclusion. Standard names and prefixes also prevent a binary-versus-decimal factor from growing into large capacity discrepancies. The compression is powerful because a symbol such as bit can carry several adjacent meanings.

Abstract Reasoning

  1. Identify the information or data quantity being expressed.
  2. Write the defining formula and its logarithm base, if applicable.
  3. Select the unit name and symbol under a declared standard convention.
  4. Convert between bases using the constant logarithm base-change factor.
  5. Separate entropy or self-information from storage positions and encoded length.
  6. Apply decimal or binary prefixes exactly as declared.
  7. Attach probability, coding, time, bandwidth, or symbol denominators required by the quantity.
  8. Check that every numerical comparison uses compatible quantity kinds and units.

Knowledge Transfer

The strict parent is Measurement: information units provide the reference scale and unit convention by which a defined target attribute is assigned a quantitative value. The domain-specific residual is the logarithmic-base family, its conversion law, and the information-versus-storage distinctions. Measurement also requires procedure and uncertainty when an empirical target is observed; a purely mathematical entropy calculation supplies its value from a stated distribution.

Relationships to Other Abstractions

Local relationship map for Units of InformationParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Units of InformationDOMAINPrime abstraction: Measurement — is a kind ofMeasurementPRIME

Current abstraction Units of Information Domain-specific

Parents (1) — more general patterns this builds on

  • Units of Information is a kind of Measurement Prime

    Measurement is the strict parent because the unit family maps a defined information attribute onto a conventional quantitative scale that enables comparison and conversion.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Units of Information sits in a sparse region of the domain-specific corpus (92nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Logarithmic Information & Scale (9 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08