Lecture notes for the Introduction to Computer Science I by James Tam

Non-Decimal Based Number Systems, Storing Numbers On The Computer And Logic

Notes for the required material

There are three main parts to this section of notes: non-decimal based number systems, the computer storage and manipulation of negative and real numbers, and logic.

The first part of this section includes a brief introduction of different number numbers starting with the familiar decimal base and continuing on to binary, octal and hexadecimal. In addition students should learn how to convert to and from decimal and a number system of any base. Finally students should learn basic mathematical operations in binary.

The second part of this section teaches students how negative and real numbers are stored and manipulated on the computer in the form of complements (one's and two's) and floating point representations. This part of the notes also deals with conversions to and from unsigned binary and the signed representations, issues such as the limits in different representations (ranges in the values that can be represented) and the problems of overflow. Finally this part of this section of notes should provide students with a strong idea of how real values are represented on the computer and some of the limits of this form of representation (accuracy).

The final part of this section of notes covers basic logical operations: AND, OR, NOT, XOR, NAND and NOR.

These notes can be purchased in the Student Union Copy Center at cost
Non-decimal based number systems (Leestma & Nyhoff Section 1.2): [PowerPoint] [Acrobat]
Numerical representations (Leestma & Nyhoff: floating point (p. 66)): [PowerPoint] [Acrobat]
Logic (Leestma & Nyhoff Section 4.2): [PowerPoint] [Acrobat]

Additional examples (some are a bit on the long side but most of them should provide good practice):

Optional teaching material

Given that there is time in lecture, the instructor can also spend some time on the following topic:

Non-decimal based math: This includes doing basic mathematical operations (addition, subtraction and multiplication) on other non-decimal based number systems besides binary (octal and hexadecimal).

Background / Sources of additional information

Pascal Programming and Problem Solving by Leestma S. and Nyhoff L. (MacMillan) Section 1.2 provides a brief overview of many of the topics to be covered in this section: non-decimal based number systems, complements and floating point representations.
Digital Design by Mano M. M. 2nd edition (Prentice Hall). This book provides a thorough coverage of this section's topics including: non-decimal based number systems, non-decimal math, complements and the different logic operations. It is done from the point of view of logic circuits and hardware.
Computer Science Illuminated by Dale N. and Lewis J (Jones and Bartlett). This book discusses many of the topics covered in this section: non-decimal based number systems, non-decimal based math (binary addition and subtraction) and converting between different number systems.
Introduction to the PDP-11 and its Assembly Language by Frank T.S. (Prentice Hall). This book covers some of the topics covered in Mano (above) such as binary and logic but the instructor may find the alternate ways that the author describes complements (diagrams) useful.
The course notes for CPSC 203 when I discussed the topics of number systems and logic: http://pages.cpsc.ucalgary.ca/~tamj/2002/203/notes/numbers.html

Teaching Tips

This is a section where the instructor should rely less on prepared slides. The online notes can be useful for described the basic concepts (e.g., binary, octal and hex) but most students will pick up the material when many examples are covered. Therefore while a few numerical examples are provided online, lectures should supplement this material with addition ones.