Problem $1($IEEE $754$ Floating Point Format$)$

IEEE $754-2008$ contains a half precision that is only $\backslash (\backslash$mathbf$\{16\}\backslash )$ bits wide. The leftmost bit is still the sign bit, the exponent is $5$ bits wide and has a bias of $15.$ The fraction is $10$ bits long. A hidden $1$ to the left of the floating point is assumed after the number is normalized. Write down the bit pattern to represent $\backslash (-71\mathrm{.}875\backslash$times $10^\{-2\}\backslash )$ assuming this format. What are the largest positive and the smallest negative numbers in terms of their absolute values it can represent $($Note: you only need to write down their bit patterns. No need to calculate their decimal values$)?$