final solutions

896 final examination name 8 c consider an input

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: omplicated one with meshes at the leaves.) Solution: ������ � since � � ��� �  6 6.896 Final Examination Name Problem 4. Short Answer (3 parts) [18 points] (a) Prove or give a counterexample. The number of latches in a synchronous circuit re­ mains invariant under retiming. Solution: This is false and counterexamples are easy to find. The correct statement is that the number of latches around a cycle is preserved. (b) Give a Gray code on �-bit numbers. Solution: 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000 7 6.896 Final Examination Name 8 (c) Consider an �-input, �-output butterfly network. Suppose that an adversary destroys a single switch in the network, preventing some inputs from connecting to some outputs in a single pass through the network. We can still find a large subset � of inputs and a large subset � of outputs such that every input in � can connect to every output in � . Let � � ��� ��� � � �� ��, where � and � are chosen to allow � to be as large as possible. Give a good asymptotic upp...
View Full Document

This document was uploaded on 03/20/2014 for the course EECS 6.896 at MIT.

Ask a homework question - tutors are online