A display has $50$x$50$ pixels, each has RGB color LEDs. The intensity value of each LED has to be transmitted serially, and the maximum bandwidth available is $1$GHz $($or $1$Gbps$).$ a$.$ If $60$ frames per second of display has to be achieved, what is the digital resolution of each LED? b$.$ What is the total number of digital pins required to make this transmission? $($assuming row select, column select, RGB select, and data$)$