$1.$a Describe the problem we end up with when encoding extremely large or extremely small fixed point numbers $($i$.$e$.$ fractions$)$ and how it is solved on a von Neumann machine.

$[3$ marks$]$

$1.$b i$.$ Convert the decimal number $18610$ to its corresponding unsigned $8-$bit binary number.

$[1$ mark$]$

ii$.$ Convert the unsigned $8-$bit binary number ${11110110}_2$ to its corresponding decimal number.

$[1$ mark$]$

iii. Convert the decimal number ${94}_{10}$ to its corresponding hexadecimal number.

$[1$ mark$]$

iv$.$ Convert the following decimal numbers to $8-$bit $2\text{'}$s complement: ${35}_{10},{80}_{10}.$ Then add them, giving the answer also in $8-$bit $2\text{'}$s complement.

$[2$ marks$]$

v$.$ Convert the following decimal numbers to $8-$bit $2\text{'}$s complement: $-4010,-5510.$ Then add them, giving the answer also in $8-$bit $2\text{'}$s complement.

$[2$ marks$]$

$1.$c i$.$ Specify the decimal number $-128$ in an $8-$bit binary sign and magnitude representation.

$[2$ marks$]$

ii$.$ Specify the hexadecimal $B{A}_{16}$ in an $8-$bit binary sign and magnitude representation.

$[2$ marks$]$

iii. Convert the decimal number $\frac{10}{322}$ to the $32-$bit IEEE $754$ floating point and express your answer in hexadecimal. $($Reminder: the $32$ bits are used as follows: Bit $1$: sign of mantissa, bits $2-9$: $8-$bits of exponent in excess $127,$ bits $10-32$: $23$ bits for magnitude of mantissa.$)$

$[6$ marks$]$

$1.$d i$.$ Describe what are the status flags, what is their purpose and where they are located in a Central Processing Unit $($CPU$)$ of a von Neumann machine.

$[2$ marks$]$

ii$.$ Name the three basic status flags that are used by the Arithmetic Logic Unit $($ALU$).$

$[3$ marks$]$