Non-Decimal Based Number Systems,
Storing Numbers In 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 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-based system and continuing on to
binary, octal and hexadecimal. In addition students should learn how to
convert to and from decimal to 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
(ones and twos) 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]
If 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) with 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.
These topics are covered from a lower level perspective than I teach in this
course (logic circuits and hardware) but it still provides a useful
grounding because higher level Computer Science courses will eventually
teaching at this levels.
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.
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.