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Binade

In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent.

Version
v1 · 2026-09-28 · History
Domain-specific #
8194
Domain group
Applied Sciences & Engineering
Origin domain
Computer Science & Software Engineering
Subdomains
Floating Point Arithmetic, Numerical Analysis → Computer Science & Software Engineering

Core Idea

Binade is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent. In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent. for some integer value e , that is, the set of real numbers or floating-point numbers x of the same sign such that.

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Doubling Number Buckets

Computers sort numbers into size groups where each group ends at double where it started. One group holds the numbers from 1 up to just before 2, the next from 2 up to just before 4, the next from 4 up to just before 8. Each of those groups is called a Binade, and the minus numbers get their own matching groups.

Same-Exponent Number Band

Computers often store numbers in a style a bit like scientific notation, but using powers of 2: a sign (plus or minus), a size setting called the exponent, and some digits. A Binade is the set of all numbers that share the same sign and the same exponent. That makes each binade a band of numbers that starts at a power of 2 and goes up to just below the next power of 2, like 8 up to just below 16. Every positive number in that band has the same exponent, and the negative band from -16 up to -8 is its own binade.

Same-Sign, Same-Exponent Band

In binary floating-point, a number is stored as a sign, an exponent, and a significand, roughly sign × significand × 2^exponent. A Binade is the set of floating-point numbers that share the same sign and exponent. For positive numbers that is usually the half-open interval [2^e, 2^(e+1)), and for negative numbers the matching interval (-2^(e+1), -2^e]. Within one binade the representable numbers are evenly spaced. Some authors use the closed interval instead, and some also treat special values such as zeros, infinities, NaN, or the range of subnormal numbers as binades of their own.

 

A Binade is the set of numbers in a binary floating-point format that share the same sign and the same exponent. For a given integer exponent e, the positive binade is conventionally the half-open interval [2^e, 2^(e+1)) and the negative one is (-2^(e+1), -2^e]; the term can refer either to the real numbers in that interval or to the floating-point numbers that lie in it. Some authors instead use the closed interval [2^e, 2^(e+1)]. Because every member of a binade uses the same exponent, the spacing between consecutive representable values is constant inside it, which makes the binade the natural unit for reasoning about rounding error and ulp size. Conventions differ at the edges: some treat zeros, infinities, and NaN each as a separate binade, and likewise the exceptional subnormal interval (0, 2^emin). The concept is used in numerical analysis and software engineering whenever an argument or test proceeds exponent by exponent.

Scope of Application

  • In other words, a binade is the interval. for some integer value e , that is, the set of real numbers or floating-point numbers x of the same sign such that.

  • In other words, a binade is the interval. Some authors use the convention of the closed interval [2^e, 2^{e + 1}] instead of a half-open interval,.

  • In other words, a binade is the interval. Some authors additionally treat each of various special quantities such as NaN, infinities, and zeroes as its own binade,.

  • In other words, a binade is the interval. or similarly for the exceptional interval (0, 2^{\mathrm{emin}}) of subnormal numbers.

  • In other words, a binade is the interval. [2^e, 2^{e + 1}) or (-2^{e + 1}, -2^e].

Clarity

A clear use of Binade names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent.

Manages Complexity

Binade compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—some authors use the convention of the closed interval [2^e, 2^{e + 1}] instead of a half-open interval,.—and the practical consequence—sometimes using both conventions in a single paper. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.

Abstract Reasoning

  1. Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent.
  3. Check operation and conditions. Some authors additionally treat each of various special quantities such as NaN, infinities, and zeroes as its own binade,. 4.

Knowledge Transfer

Within the home domain. Knowledge about Binade transfers literally when a new case preserves the same carrier type, relation, and recognition test. for some integer value e , that is, the set of real numbers or floating-point numbers x of the same sign such that. Some authors use the convention of the closed interval [2^e, 2^{e + 1}] instead of a half-open interval,. Beyond the home domain. No canonical parent is asserted for Binade.

Neighborhood in Abstraction Space

Binade sits in a crowded region of the domain-specific corpus (22nd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Algebraic Structures & Order Relations (18 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08