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. In other words, a binade is the interval $$[2^e, 2^{e + 1})$$ or $$(-2^{e + 1}, -2^e]$$ for some integer value $$e$$, that is, the set of real numbers or floating-point numbers $$x$$ of the same sign such that $$2^e \leq |x| < 2^{e + 1}$$.

Some authors use the convention of the closed interval $$[2^e, 2^{e + 1}]$$ instead of a half-open interval, sometimes using both conventions in a single paper. Some authors additionally treat each of various special quantities such as NaN, infinities, and zeroes as its own binade, or similarly for the exceptional interval $$(0, 2^{\mathrm{emin}})$$ of subnormal numbers.