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The Butterfly network is an interconnection network composed of log p levels (as the omega network). In a Butterfly network, each switching node i at a level l is connected to the identically numbered element at level 1 + 1 and to a switching node whose number differs from itself only at the Ith most significant bit. Therefore, switching node S is connected to element S, at level 1 if j = i orj = i 2logp- A. Consider a Butterfly network with eight processing nodes connected to eight memory banks: i. (10 points) How many stages are needed? ii. (25 points) Sketch the network showing input, output, as well as switching nodes. iii. (15 points) What is the diameter and bisection width of this network? Explain your answer iv. (10 points) knowing that messages in butterfly network are self-routed. In other words, each stage uses one destination bit for routing purposes where "0" means route up and "1" means route down. Show the routing of a message from node 0 to node 4. The Butterfly network is an interconnection network composed of log p levels (as the omega network). In a Butterfly network, each switching node i at a level l is connected to the identically numbered element at level 1 + 1 and to a switching node whose number differs from itself only at the Ith most significant bit. Therefore, switching node S is connected to element S, at level 1 if j = i orj = i 2logp- A. Consider a Butterfly network with eight processing nodes connected to eight memory banks: i. (10 points) How many stages are needed? ii. (25 points) Sketch the network showing input, output, as well as switching nodes. iii. (15 points) What is the diameter and bisection width of this network? Explain your answer iv. (10 points) knowing that messages in butterfly network are self-routed. In other words, each stage uses one destination bit for routing purposes where "0" means route up and "1" means route down. Show the routing of a message from node 0 to node 4