Floating-point numbers

A set of numbers consistent of zero and all numbers of the form:

\[ \pm (1 + f) \times 2^n, \] where \(n\) is an integer called the exponent, and \(1+f! is the **mantissa** or **significand**, in which\)$ f = _{i=1}^d b_i2^{-i}, b_i {0,1}, $$ for a fixed integer d called the binary precision

In base 10 we get scientific notation with \(d+1\) sig. digits

\[ \pm(b_0 + \sum_{i=1}^d b_i10^{-i}) \times 10^n = \pm(b_0 b_1 b_2 \cdots b_d) \times 10^n, \] where \(b_i \in \{0,1,...,9\}\) and \(b_0 \neq 0\).