$11.(18\%)($Pipelining and parallelism Design Probelm$)$

You have been given the task of designing a new media chip for HD applications. Specifications call for the rendering of a $2000$x$1000$ pixel image at $100$Hz$,$ With a single module, it takes $10$us to process one pixel, and treg is $0$ps$.$

$($a$)$ What is the throughput needed, in pixels per second, for this task?

$($b$)$ Your coworker suggests making one long pipeline. Can you do this and still meet your throughput goal? If so$,$ how many stages does it require? If not, why not?

$($c$)$ Why could $($a$)$ be a bad idea?

$($d$)$ Another coworker suggest just replicating the processing module; how many do you need?

$($e$)$ Why this be a bad idea?

III. Design problem

$11.(18\%)($Pipelining and parallelism, $3$ points for each question$)$

You have been given the task of designing a new media chip for HD applications. Specifications call for the rendering of a $20001000$ pixel image at $100Hz,$ With a single module, it takes $10$ us to process one pixel, and treg is $0$ps$.$

$($a$)$ What is the throughput needed, in pixels per second, for this task?

$($b$)$ Your coworker suggests making one long pipeline. Can you do this and still meet your throughput goal? If so$,$ how many stages does it require? If not, why not?

$($c$)$ Why could $($a$)$ be a bad idea?

$($d$)$ Another coworker suggest just replicating the processing module; how many do you need?

$($e$)$ Why this be a bad idea?

$($f$)$ After talking to the logic designers, you decide to use replicated ten$-$stage pipelined. How many do you need?$($f$)$ After talking to the logic designers, you decide to use replicated ten$-$stage pipelined. How many do you need?