NVIDIA has a "half" format, which is similar to IEEE $754$ except that it is only $16$ bits wide. The leftmost bit is still the sign bit, the exponent is $5$ bits wide and the Fraction field is $10$ bits long. A hidden $1$ is assumed.

REPRESENTATION RANGE OF THE NVIDIA 'HALF FORMAT'

For each of the following, write the binary value and the corresponding decimal value of the $16-$bit floating point number that is the closest available representation of the requested number. If rounding is necess $2$ ary use round$-$to$-$nearest. Give the decimal values either as whole numbers or fractions.

$($i$)$ The number $\text{'}0\text{'},$ Charge of an electron $(-1\mathrm{.}6{10}^{-19}),$ smallest positive normalized number, smallest positive denormalized number, largest positive normalized number, largest positive denormalized number, distance b$/$w Earth and Neptune in inches: $171,072,000,000,000$