9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU1 Course Overview First Material

9/15/09 - L1 Crs Ovrvw Copyright 2009 - Joanne DeGroat, ECE, OSU 1

Course OverviewFirst Material


Class 1 outline Course Syllabus Information Representation Number Systems

Material from sections 1-1 and 1-2 of text

Personal course website ece.osu.edu/~degroat

Information Representation In the real world

Items that we want to measure are continuous, i.e., they can have any value Weight Temperature Pressure Velocity And many, many others


But in a computer The paradigm of a computer that we are

familiar with is electronic. But there have been others like Babbage’s compute engine and cash registers which were mechanical.

The electronics make it easy to represent two states, on and off, or high voltage level and low voltage level.


Realization Result: representation of real world quantities

by a system that can only represent discrete states, and thus discrete quantities.

Example Use you fingers to represent temperature from

10oF to 100oF. What values did you represent?


Realization Result: representation of real world quantities by

a system that can only represent discrete states, and thus discrete quantities.

Example Use you fingers to represent temperature from 10oF

to 100oF. What values did you represent? Ans: partially depends on whether it was in 8 or 10

steps. So it was either in 10oF steps or 12.5oF steps.9/15/09 - L1 Crs Ovrvw Copyright 2009 - Joanne DeGroat, ECE, OSU 6

Digital Systems Digital electronics have progressed from 12V

logic elements to 1.2V logic elements. Could use these values OR Use a representation of 1 for a HIGH And a representation of 0 for a LOW

In electronics we restrict ourselves to just these two states to provide interpretation of a range of voltages as HIGH or a 1 and another range as LOW or a 0. Why?


The Digital Computer “Virtually every aspect of digital system

design is encompassed in a computer design” (Hill and Peterson)

“Computers are the most important type of digital sytem”

Computers and digital systems have become pervasive in our world From cell phones to MP3 players to ……


Computers & digital systems today There everywhere, there everywhere

PCs and Workstations Cell phones MP3 players Cameras Your automobile – an automobile will have 15 to 40

embedded processors Microwaves Stoves, Dishwashers, fautces (auto temp control) Washers, Dryers, Vacuum cleaners And on and on and on and on and ………….


The computer Major components

The CPU – central processing unit – the datapath combined with the control unit Datapath – performs the actual arithmetic and logic

functions on the data Control Unit – THE BRAIN – controls the flow of data

and instructions, decoding and executing instructions MEMORY – Consists of both registers, main

memory and secondary memory I/O or Input/Output – communication channels to get

information into and out of the computer


Computers and digital systems Each of the components of “The Computer”

is a digital component “The computer” consists of an interconnected

set of digital modules. Most of the components is are designed with

not much more than the techniques of this class.


Number Systems In digital systems you can only represent 2

states. A base 10 number systems is simply not

straightforward.

Will need a different number system. Concepts across number systems are the

same.


General number systems A number system has a base or radix, r A number in base r contains digits 0,1,2,…,r-1 The value represented as a power series in r as

An-1rn-1 + An-2rn-2 + … + A1r1 + A0r0 +

A-1r-1 + A-2r-2 + … + A-mr-m

and is written An-1 An-2 …A1 A0 . A-1 A-2 …A-m


General number systems (2) The “ . “ is called the radix point.

In base 10 it is the decimal point In base 2 it is the binary point

is referred to as the most significant digit Referred to as the msb

is referred to as the least significant digitReferred to as the lsb Usually m=0 so is the lsb


For base 10 or radix 10 Example - book 724.5 421

From prior education may have referred to digits as the units, tens and hundred positions

421 = 4.21 x 102 in scientific notation 421 = 4 x 102 + 2 x 101 + 1 x 100

(Recalling that anything to the 0 power is 1)


Something in base or radix 5 (123)5 What is it’s value?

(Note method of showing base of number) Value

Val (123)5 = 1 x 52 + 2 x 51 + 3 x 50

= 25 + 10 + 3 = (38)10


Binary numbers – base or radix 2 Have binary digits 0 and 1 So all number represented in binary have only

digits 0 and 1 11010 would have value?

= 1 x 24 + 1 x 23 + 0 x 22 + 1 x 21 + 0 x 20 + = 1 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 0 x 1 = 16+8+2 = (26)10


Know the powers of two The first 16 powers of two are in the

following table.


n 2^n n 2^N

0 1 8 256

1 2 9 512

2 4 10 1024

3 8 11 2048

4 16 12 4096

5 32 13 8192

6 64 14 16384

7 128 15 32768

Some common size terms 210 is commonly referred to as kilo or K 220 is commonly referred to as mega or M 230 is commonly referred to as giga or G 240 is commonly referred to as tera or T

So 4K is = 22 x 210 = 212 = 409610


Base 10 to binary One method

Subtract the largest power of two from the value and repeat until done.

Text example 652 146

Largest if 128 or 27 leaving18 Then have 16 or 24 leaving just 2 Which is 21 giving value 1 0 0 1 0 0 1 0


Fractional Parts In base 10

Have xx.12 which is 1 x 10-1 + 2 x 10-2 In base 2

Have binary point xxx.1 which is 1 x 2-1 or 0.5 (1/2) And xxx.01 which is 1 x 2-2 or 0.25 (1/4) And xxx.001 which is 1 x 2-3 or 0.125 (1/8) And xxx.0001 which is 1 x 2-4 or 0.0625 (1/16)


In digital systems and computer Have two other radix systems that are related

to binary or base 2 as they are powers of it. Octal or base 8

Can get an octal representation by grouping a binary number into groups of 3 digits.

Octal numbers use 8 distinct digits 0 through 7 110010 = 110 010 = (6 2)8 for example And can use same general number systems

expansion shown earlier.


Hex Hex or Hexadecimal is more common than

Octal representation today Hex is base or radix 16 Thus group 4 binary digits 1111 0100 1011 would be?

F 4 B For representation need 16 symbols

Use 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F


Class 1 assignment Read sections 1-1 and 1-2 Problems for hand in

1-4, 1-8, 1-9 Problems for practice

1-10, 1-11

Reading for next class sections 1-3 and 1-4


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9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU1 Course Overview First Material