IEEE $754-2008$ contains a half precision that is only $16$ bits wide. The leftmost

bit is still the sign bit, the exponent is $5$ bits wide and has a bias of $15,$ and the

mantissa is $10$ bits long. A hidden $1$ is assumed. Write down the bit pattern to

represent $-12\mathrm{.}223$ assuming a version of this format, which uses an excess$-16$

format to store the exponent. Comment on how the range and accuracy of this

$16-$bit floating point format compares to the single precision IEEE $754$ standard.