In the decimal system we would write a number like \( 9.90625 \) in what is called the normalized scientific notation. $$ 9.90625=0.990625\times 10^{1}, $$ and a real non-zero number could be generalized as $$ \begin{equation} x=\pm r\times 10^{{\mbox{n}}}, \tag{1} \end{equation} $$ with \( r \) a number in the range \( 1/10 \le r < 1 \). In a similar way we can use represent a binary number in scientific notation as $$ \begin{equation} x=\pm q\times 2^{{\mbox{m}}}, \tag{2} \end{equation} $$ with \( q \) a number in the range \( 1/2 \le q < 1 \). This means that the mantissa of a binary number would be represented by the general formula $$ \begin{equation} (0.a_{-1}a_{-2}\dots a_{-n})_2=a_{-1}\times 2^{-1} +a_{-2}\times 2^{-2}+\dots+a_{-n}\times 2^{-n}. \tag{3} \end{equation} $$