$<3\mathrm{.}5>$ IEEE $754-2008$ contains a half precision that is only $16$ bits

wide. The left most 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 $1\mathrm{.}5625$ x $10^-1$ 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.