Answer the following questions. $(10$ pts$)$

a$)$ Mathematically prove that for an oscillator frequency of $16MHz,$ SPI communication is faster than the UART in high$-$

speed mode.

b$)$ Using the formula and subsequent steps, show that to generate a baud rate of $28800$ in the high speed UART mode,

SPBRG value is $42.$

c$)$ Consider delay generation of $5$ microseconds using Timer $2.$ If Fosc$=16MHz$ and $T2$CON$=014,$ calculate the values

of TMR$2$ and PR$2.$ Clearly write the formula used to calculate this and show the substitutions in the formula. If $5$

microseconds is the delay generated before the post$-$scaler, what is the total time elapsed before the interrupt is

triggered?

d$)$ RCSTA$=11010001\mathrm{.}8$ bits of data received are $10101101$ and the $9^{th}$ bit in this case is a parity bit. Based on this, is the

received data potentially accurate? Justify your answer.