Q$1[40$ Points$].$ For a daisy$-$chained SPI with $4$ devices $($C $$ Device #$1$ Device #$2$ Device #$3$ Device #$4),$ the

SPI master intends to send the following bytes to the devices in sequence:

$0$x$5$A to Device #$1$

$0$x$6$B to Device #$2$

$0$x$7$C to Device #$3$

$0$x$8$D to Device #$4$

Additionally, at the start of communication, all devices hold the byte $0$xFF in their SPI shift registers.

$($Part $1)$ After $32$ clock cycles, what will be the contents of the SPI shift registers of devices?

$($Part $2)$ If the SPI clock operates at $500$ kHz$,$ how long $($in milliseconds$)$ will it take for the SPI master to complete the

transmission to all devices and receive back the first byte sent?

$($Part $3)$ Suppose the master sends the byte sequence with an incorrect clock frequency of $250$ kHz$,$ but the devices

expect $500$ kHz$.$ What would be the potential impact on the data received by Device #$4,$ and why?

$($Part $4)$ If Device #$2$ is configured to reverse the bits of the data it receives before passing it on$,$ what will be the final

byte received by the master after $32$ clock cycles?

Q$2[40$ Points$].$ You are designing a system to control the brightness of an LED using timer$-$based Pulse Width Modulation

$($PWM$)$ on a microcontroller.

$($Part $1)$ Calculate the period of a PWM signal with a frequency of $1$ kHz in microseconds. The microcontroller$$s clock

frequency is $16$ MHz$,$ and the timer uses a prescaler of $64.$ Calculate the value to be loaded into the timer$$s register

$($TA$0$CCRx value$)$ to achieve a $1$ kHz PWM frequency.

$($Part $2)$ Given the calculated TA$0$CCRx value from part $(1),$ compute the TA$0$CCRx for the $50\%$ and $75\%$ duty cycle.

$($Part $3)$ Assume the timer is in $8-$bit mode $(255$ max$).$ Calculate the minimum and maximum achievable PWM fre$-$

quencies using the $16$ MHz clock and a prescaler of $64.$ Determine the resolution of the duty cycle as a percentage.

$($Part $4)$ Suppose you switch to a $16-$bit timer with the same $16$ MHz clock and a prescaler of $64.$ Calculate the

maximum TA$0$CCRx value. Calculate the minimum achievable PWM frequency.

Q$3[20$ Points$].$ A push button is used to control an LED based on these rules: $(1)$ Every time the push button is pressed,

the LED turns ON for $5$ seconds; $(2)$ If the button is pressed again within the $5-$second window, the timer resets, and the

LED stays ON for another $5$ seconds from the latest press. A user interacts with the button as follows:

$$ Press $1$: Time $=0$ seconds

$$ Press $2$: Time $=3$ seconds

$$ Press $3$: Time $=8$ seconds

$$ Press $4$: Time $=12$ seconds

$($Part $1)$ Calculate the total time the LED stays ON based on the button press sequence. Provide a timeline showing

the ON and OFF states of the LED.

$($Part $2)$ Explain if there are any periods where pressing the button has no effect and why that happens.

$($Part $3)$ Consider a scenario where the button is pressed every $4$ seconds starting at Time $=0$ seconds. How long

would the LED remain ON by the $20$th press?