Q43

The following is a scheme for floating point number representation using $16$ bits.

Let $s, e,$ and $m$ be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is: $\begin{cases}(-1)^s \left(1+m \times 2^{-9}\right) 2^{e-31}, & \text{ if the exponent } \neq 111111 \\ 0, & \text{ otherwise} \end{cases}$ What is the maximum difference between two successive real numbers representable in this system?