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Unformatted text preview: CSc 445: Homework Assignment 3 Assigned: Monday Feb 18 2008, Due: 10:30 AM, Monday March 3 2008 Clear, neat and concise solutions are required in order to receive full credit. Revise your work carefully before submission, and consider how your work is presented. If you cannot solve a particular problem, state this clearly in your write-up, and write down only what you know to be correct. For involved proofs, first outline the argument and then delve into the details. 1. (20 pts) Traditionally, we talk about numbers in decimal, binary, octal, and other (positive) bases. However, it is possible to use negative numbers, and there are several advantages in this approach. For example, there is no need for a sign bit, as both negative and positive numbers can be represented. Consider the case where -2 is used as a base. The digits needed are 0 and 1 as in regular binary notation but the interpretation is different; 1101 is -3 and 10010 is 14 because: ( a n . . . a 2 a 1 a ) = a n ( 2) n + + a 2 ( 2) 2 + a 1 ( 2) 1 + a . (a) What is the procedure for finding the base -2 notation of a given (decimal) number? (b) Prove that the 2 n possible bit patterns in an n-bit word in base -2 uniquely represent all integers in a certain range. (Hint: first determine the range and then use induction)....
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- Spring '08