hw4 - CS 6143 COMPUTER ARCHITECTURE II HOMEWORK IV FALL...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 6143 COMPUTER ARCHITECTURE II FALL 2010 HOMEWORK IV Polytechnic Institute of NYU Page 1 of 18 Handout No : 7 October 20, 2010 DUE : November 10, 2010 READ : . Related portions of Chapters 2, 3, 4 and Appendces E and H of the Hennessy book . Related portions of Chapter 1, 4 and 6 of the Jordan book ASSIGNMENT: There are two problems. Solve all homework and exam problems as shown in class and past exam solutions. 1) Draw three different interconnection networks with 64 nodes : . A cube-shaped three-dimensional torus network, . A hypercube network and . A cube-connected-cycles (CCC) network. Indicate, by explaining : . The degree, . The diameter, . The total number of links, of each network, . For the given size of the networks and . For any size. For the three networks, you need not show all the links and node numbers. But, show enough to give an idea about the pattern of link connections and node numbering. 2) Draw a Benes network with 8 nodes on each side. Í Describe its unique features and show how messages would travel from one side to the other. RELEVANT QUESTIONS AND ANSWERS Q1) On a 3-CCC, embed the largest ring possible. That is, form the longest path possible that starts at node “a” and ends at node “a,” forming a circle (ring). To show the embedded ring, number the nodes of the 3-CCC and write down the order of the nodes traversed when the embedded ring is traversed.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Polytechnic Institute of NYU Page 2 of 18 CS6143 Handout No : 7 October 20, 2010 A1) The 3-CCC has 24 nodes. Each node has a unique address : (i, j) where “j” indicates which corner of the 3-CCC the node resides at and “i” indicates which node of the corner. To form a 3-CCC, we connect node (i,j) to node (i,m) if and only if “m” is the result of inverting the “i” th bit (from left, starting at 1) of the binary representation of “j.” For example, for node (1,3), the connection to the next corner is to node (1,7). Because, “i” is 1 and “j” is 3 (or 011). “m” is 7 (111) since we invert bit one from left of “j.” Below is the 3-CCC with the ring embedded : The ring includes all the nodes of the 3-CCC and can be traversed in many ways : with different starting points and different paths. All of these long rings have the same length : 24 links. This ring is shown by thick lines in the above picture. Here is one ring starting at (2,1) : (2,1)-(2,3)-(1,3)-(3,3)-(3,2)-(2,2)-(1,2)-(1,6)-(2,6)-(3,6)-(3,7)-(1,7)-(2,7)-(2,5)-(1,5)-(3,5)-(3,4)-(2,4)-(1,4)-(1,0)- (2,0)-(3,0)-(3,1)-(1,1)-(2,1). Q2) Consider the following static direct interconnection network : (3,1) (2,1) (1,1) (3,0) (1,0) (2,0) (1,4) (2,4) (3,4) (2,2) (1,2) (3,2) (3,5) (2,5) (1,5) (2,6) (1,6) (3,6) (3,7) (2,7) (1,7) (3,3) (2,3) (1,3) starting point Apex Level 2 Level 1 Level 0 Base This is a pyramid network of size k 2 or size 16. Make observations on the network, including (i) the number of nodes, (ii) the degree, (iii) the diameter and others as a function of k based on the discus- sion of interconnection networks in class. Note that in the pyramid network, all, except base nodes, have four children each, on the level below.
Background image of page 2
Polytechnic Institute of NYU Page 3 of 18 CS6143 Handout No : 7 October 20, 2010 A2) A pyramid network combines the advantages of mesh and tree networks and physically “puts them together.” A k 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/02/2011 for the course CS 6143 taught by Professor Hadimioglu during the Fall '10 term at NYU Poly.

Page1 / 18

hw4 - CS 6143 COMPUTER ARCHITECTURE II HOMEWORK IV FALL...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online