Lets first understand whats given in the question:
A Non-Pipelined Processor is given with 25ns and latency modules are: 2,3,4,7,3,2,4 (in ns). If this processor is pipelined then the conditions to keep in mind are not to rearrange the order of modules and not to divide a module into multiple pipeline stages.
Latency of latches = 1ns. And we have been asked to consider the fewest number of stages that allows to achieve the minimum latency.
So to get fewest no. of stages we gotta combine any consecutive stages such that maximum stage latency would not exceed 7ns and the latency would be the lowest.
One of the possible combination could be: (2 + 3), 4, 7, (3 + 2), 4 = 5, 4, 7, 5, 4 ← max latency is 7(condition gets satisfied).
Therefore no. of stages, K = 5.
and the latch latency = 1 ns.
Hence, the latency of the pipeline would be,
= no. of stages * (max. latency among stages + latch latency) ns
= 5*(7 + 1) ns
= 40ns (c)
