Consider a message passing system, where N processors are connected together with an interconnection network like the figure below. As the figure shows, each N/2 of processors are connected in a 4-D hypercubes, and then the two hypercubes are connected together using a bus. Imagine that only one node from each hypercube is connected to the bus. This means that all communication to the other hypercube has to traverse through that one node.

a. What is the number of processors, N?

b. What is the bisection width of this network?

C. What is the total cost of this network?

d. What is the distance between the farthest nodes of this network?

e. Imagine that this system works with cut-through routing and we want to send a 4-word message between the 2 farthest nodes in this network (the 2 nodes with the longest distance). if the per-hop time is 10miliseconds (ms) and the packet overhead time is 1ms per word, find the total communication time for sending this message.

Bus 4D Hypercube 1 4D Hypercube 2