The following is a scheme for floating point number representation using 16 bits.
| Bit Position | 15 | 14 .... 9 | 8 ...... 0 |
|---|---|---|---|
| s | e | m | |
| Sign | Exponent | Mantissa |
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?
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