$($a$)$ Consider a system to display the digits a$,$ b$,$ c$,$ d on a $7-$segment LED when

the inputs are $0,1,2,$ and $3$ respectively, as shown in figure $1,$ where $x_1{x}_2$

represents the binary number of the input value. Write down the truth table

and the corresponding logical functions.

$5$

$Z_i=f_i(x_1,x_2),i=1,$cdots,$7$

$($b$)$ Write down the equation governing the relation between program execution

time and clock rate. $[1]$

Given two CPUs, XPU$1$ and XPU$2.$ XPU$1$ runs at $4GHz$ while XPU$2$ runs at

$3GHz.$ Which is faster? Explain.

$($c$)$ Explain why stack pointer is not used in accessing the local variables and func$-$

tion parameters in a stack frame? $[2]$

Show how displacement addressing can be used for this purpose. $[2]$

$($d$)$ Most arithmetic operations require $3$ operands, two source operands and one

destination operand. Explain where the operands are for two$-$operand, one$-$

operand, and zero$-$operand instructions. $[3]$

$($e$)$ A CPU executes in either user mode or supervisor mode. In which mode is

a user program and the Operating System running? How can a user program

switch to supervisor mode to access system services?