$1.$ The IEEE$754$ half$-$precision floating$-$point format is a

$16-$bit half$-$word divided into a $1-$bit sign indicator s$,$

a $5-$bit biased exponent e$,$ and a $10-$bit fraction f$.$

The exponent values $00000$ and $11111$ are reserved.

The exponent bias is $15.$ And a hidden $1$ is assumed.

a$.$ Express the $16-$bit pattern for the smallest possible magnitude $($positive non$-$zero number$).$ Use $0,1,$

and X$,$ which the latter represents a $$does not matter$$ condition.

b$.$ Determine the decimal value $($base$-10)$ of the smallest possible magnitude from part a$.$

c$.$ Given the bit pattern for a $16-$bit floating$-$point number, first find the real binary number with its radix

point and binary fraction as needed.

bit pattern $=1001111001100110$

Then convert the number to a real decimal number with its decimal point and decimal faction as

needed.

d$.$ Determine the binary encoding for the number $(3\mathrm{.}625)10$ using the $16-$bit floating$-$point number

format. Hint: first convert the unsigned number to binary with its radix point and binary fraction.

e$.$ Give the bit pattern for a $16-$bit floating$-$point number that represents positive infinity.