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 $b_0 \neq 0$.