Floating-point representation ($(-1{)}^{s}m{\beta }^e$)

A finite normal floating-point representation stores a sign, a significand and a bounded integer exponent, representing $(-1{)}^{s}m{\beta }^e$ in radix $\beta$. Fixing the number of significand digits gives roughly constant relative precision across a wide dynamic range; the gap between adjacent representable values grows with the exponent.

For example, $6.5=1.101_2{2}^2$ in the binary numeral system. The normal leading binary digit is one and can be implicit in storage. Subnormal numbers use a different leading-digit rule near zero. IEEE formats also reserve encodings for signed zero, infinities and NaN, so the bit pattern cannot always be interpreted by the normal finite formula.^[ref]

The significant-digit factor $m$ in a floating-point representation $(-1{)}^{s}m{\beta }^e$, where $s$ is the sign bit, $\beta$ the radix and $e$ the exponent. For a normal positive binary significand, $1\le m<2$, and the leading one need not be stored. In a subnormal number, the leading digit is zero at the minimum normal exponent scale. The significand is a numerical factor, distinct from the stored trailing fraction bits that encode part of it.