A PIC$24$ processor is interfaced to an LCD according to the following IO mapping:

$\begin{array}{cc}\text{P}\text{r}\text{o}\text{c}\text{e}\text{s}\text{s}\text{o}\text{r}& \text{L}\text{C}\text{D}\\ RB7..RB0& DB7..DB0\\ RB0& RS\end{array}$

$\begin{array}{cc}\text{P}\text{r}\text{o}\text{c}\text{e}\text{s}\text{s}\text{o}\text{r}& \text{L}\text{C}\text{D}\\ RB1& \frac{R}{W}\\ RB2& E\end{array}$

Assumptions:

A processor speed is: Fosc$=50MHz.$

Timing parameters are:

TAS$(min)=50ns,$ PWEH $(min)=220nsTDSW(min)=90ns.$

Each C statement executes in one cycle

$($a$)$ Write a function that writes a byte to the LCD.

$($b$)$ Based on your code, how much time $($in seconds$)$ is needed to write $1000$ bytes to the LCD