Assume a $1$ MHz clock frequency. Explain your computations for the following questions:

a$)$ How long is the delay introduced by a single call of the following subroutine Delay$1$ in seconds when D$2$INIT $\backslash (=0\backslash$times $00\backslash )$ and D$2$INIT$=0$x$01?$

b$)$ How long is the delay introduced by a single call of the following subroutine Delay $2$ in seconds?

c$)$ Find a set of initial values for the registers dly$1,$ dly$2,$ dly$3,$ and dly$4$ so that the Delay$2$ subroutine takes $2\mathrm{.}0$ seconds with a $\backslash (1\backslash \%\backslash )$ error margin.

$2)$

Write the Assembly code to initialize Port B bits $3$ and $6$ to outputs and bit $5$ to input. Then, write the code to read button $5$ from port $\backslash ($ B $\backslash )$ and display it at bit $6$ and its complement at bit $3$ of the same port.

$3)$

What is the largest number of nested subroutine calls that can be implemented on an ATmega$32$ microcontroller without any external memory? How about with full external memory?

$4)$ Consider the following code to answer the following questions. Assume that each call of long$\_$delay takes $100$ milliseconds, and all other code takes no time at all. LOOP:

NO$\_$PRESS:

a$)$ Describe the situation that results in the shortest delay between any button on PinD being pressed and the LEDs turning off. Write down a timeline to show which code the processor executes and when. $($For example: $\backslash (\backslash$mathrm$\{$t$1\}\backslash )-$ t$2$: display complement of bit$0$; t$2-$ t$3$: long$\_$delay; t$3-$ t$4$: display complement of bit$1$; $........)$

b$)$ Describe the situation that results in the longest delay between any button on PinD being pressed and the LEDs turning off. Write down a timeline to show which code the processor executes and when.

c$)$ Describe the situation that results in the longest time that button can be pressed $($and then released$)$ without the LEDs turning off. Write down a timeline to show which code the processor executes and when.

d$)$ Modify the code to run button readings and LED output in a more concurrent way by using FSM$-$based tasks.