Machine learning and graphics workloads generally tolerate much lower precision than traditional scientific programs. As a result, IEEE has expanded the IEEE $754$ standard to include a $16-$bit FP$,$ aka FP$16$

The factional part of FP$16$ is like its $32-$bit and $64-$bit counterparts $($i$.$e$.,$ it assumes a $1.$ in $1.$fraction$).$ The exponent is also biased similarly to FP$32$ and FP$64,$ except the bit$-$width of the exponent is different. Hence, the bias value is different. What bias value should be used in FP$16$ to keep it consistent with FP$32$ and FP$64?$

Using the FP$16$ format described above, what is the closest representation of $4096\mathrm{.}6?$ Express your answer in HEX, and drop all leading $0$s$.$