CPSC 217: Assignment 3

Due Friday November 8 at 4 PM.

New Concepts to be applied for the assignment

• Problem decomposition using functions

Introduction

Floating point is the computer approximation of a real number. The number is stored in three parts: one bit for the sign (zero = positive, one = negative), a number of bits for the mantissa (the digits of the number to be stored) and the exponent (which determines the number of places that the decimal point will 'float' (from which comes the term floating point). The sign of the exponent specifies the direction of the shift when converting from floating point back to the original number. A negative exponent indicates a left shift while positive exponent indicates a right shift. Note: The sign of the exponent is not the same as the sign of the original number!  Because the mantissa can only store a fixed number of digits it is possible that precision may be lost. Like the program you are to implement the following examples will use a 5 digit mantissa.

Example 1 (number to be stored as float: 12345):
Sign bit: 0 (positive)	Mantissa: 12345	Exponent: 0	Number restored from floating point: 12345

 

Example 2 (number to be stored as float: -1234567):
Sign bit: 1 (negative)	Mantissa: 12345	Exponent: 2	Number restored from floating point: -1234500

 

Example 3 (number to be stored as float: -12):
Sign bit: 1 (negative)	Mantissa: 12000	Exponent: -3	Number restored from floating point: -12

Assignment description

Write a program that will prompt the user to enter an integer - your program does not have to allow the user to enter real numbers - the number will be stored in simulated floating point format¹. (Although it may seem strange to exclude fractional numbers in an assignment that is supposed to store a number in floating point format  the real number requirement was excluded because you may end up with errors not due to a logic of your program but because the original number was not correctly stored as float). You can assume that the input will range from the smallest possible nine digit negative number to the largest possible nine digit  positive number. The program will then represent this number in a simulated floating point form: <sign bit> <five digits for the mantissa unsigned - the sign bit stores the sign>. <signed exponent>. With only five digits for the mantissa, numbers that consist of more digits may not be stored correctly! The program will then 'reassemble' the number from the floating point representation. It should display the original number, it's floating point representation and finally the number that has been restored from the floating point representation (see Figure 1).

Figure 1A: Sample execution (positive exponent, right shift)

Figure 1B: Sample execution (negative exponent, left shift)

Submitting your work:

1. Source code Python program/'dot-py' file(s) must be electronically submitted according to [submission submission requirements].
2. Copying/viewing other student's work will be regarded as academic misconduct (cheating). For additional details about what is and is not okay for this class please refer to the following [misconduct link].
3. Before you submit your assignment here is a checklist of items to be used in marking: [checklist link]
   

External libraries that can be used (unless listed don't assume you can use an external library)

• Libraries that allow for text-based (console) input and output.
• String functions that were covered in class