CBP 2005-6Comp 1017 Digital Technologies1. CBP 2005-6Comp 1017 Digital Technologies2.

CBP 2005-6 Comp 1017 Digital Technologies 1


Patron Saint of

England,

Moscow,

Boy Scouts,

the Italian calvary, chivalry, Istanbul,

Aragon,

Beirut,

Portugal,

Germany,

Genoa,

and Venice.

In the East, he is the patron of soldiers, and also of husbandmen …

Representation

Dr.C Comp 1017


… Representations

Images

Characters

234.25

Numbers

Music

electronics

http://images.google.com/imgres?imgurl=www.ops.dti.ne.jp/~coredump/graphics/transistor.gif&imgrefurl=http://www.ops.dti.ne.jp/~coredump/povray.html&h=240&w=320&prev=/images%3Fq%3Dtransistor%26start%3D100%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8


Bits and Electronics

1 0 0 1

8s 4s 2s 1s

8 + 0 + 0 + 1 = 9

Example 1

1 0 0 1

Electronics … a wire can be on (“1”) or off

(“0”)

Electric signals

The Magic … numbers are bits

are electric signals


Numbers are Bits128 64 32 16 8 4 2 1

1 0 1 0 1

1 x 16 + 0 x 8 + 1 x 4 + 0 x 2 + 1 x 1

128 64 32 16 8 4 2 1

0 1 1 1 1

? x 16 + ? x 8 + ? x 4 + ? x 2 + ? x 1

example

question


Counting in Binary

1s2s

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

4s

0 1 2 3 4 5 6 7


CPU Mem I/O

Application

Functional Blocks

Transistors

http://images.google.com/imgres?imgurl=www.ops.dti.ne.jp/~coredump/graphics/transistor.gif&imgrefurl=http://www.ops.dti.ne.jp/~coredump/povray.html&h=240&w=320&prev=/images%3Fq%3Dtransistor%26start%3D100%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8


N-MOS

in

P-MOS

in

CMOS : Complementary

Transistors


N-MOS

In = 0 In = 1

P-MOS

In = 1In = 0

Transistors are Switches


1

0

in out

Transistor Symbols

Logic Gate Symbol

Representing Electronics


1

0

1 0

1

0

0 1

on

off on

off


1

0

B

A B

A

out

1

0

A B O

0 0

0 1

1 0

1 1

AND gate

A

B

O/P

X


Digital Logic Gates.

AND gate

A

B

O/P

A B O

0 0

0 1

1 0

1 1

LOGIC SYMBOL

TRUTH TABLE

0

0

0

1


Digital Logic Lab

A B O

0 0 0

0 1 0

1 0 0

1 1 1

input switches

A

B

O OR gate

NOT gate

NOR gate

NAND gate


Combinations of Gates

3 4

bU1

Inverter

3 4

bU1

Inverter

Sum is greater than the parts


Exercise - Find the Truth Table

A

B

C

A B C O

0 0 0

0 1 0

1 0 0

1 1 0

0 0 1

0 1 1

1 0 1

1 1 1

P

0

0

0

1

0

0

0

1

0

0

0

0

0

0

0

1

P O

AND gate AND gate


Investigation of Single Neurons

Microelectrode recording of Biological Neuron activation using tungsten electrode

Hubel and Weisel. Nobel Prize 1958

Photomicrograph: Height = 1mm.


Biological AND and NOT

0

1 1

1

1

Neuron output fires only if both inputs are 1

INHIBITORY synapse : Input high 1 prevents neuron firing

Inhibitory synapse


Two Gate Memory Cell

12

aU1

3 4

bU1

3 4

bU1

Electronic Inverter

1 00 1

Two inverters + feedback

12

aU1

3 4

bU1 1 0

0 1 0

0 1

1

Choose input 0 or 1. Follow it through two invertors with feedback. States are consistent. Two possible solutions. These are two memory states.


SRAM Memory Cell

12aU1

3 4bU1

12aU1

3 4bU1

select

select

In/out bit

In/out bit

12

aU1

3 4

bU1

Two inverters + feedback

Neural Circuits

SRAM Memory 0

1


STM and LTM

Before Learning

After Learning

A

A

B

B

Short Term Memory :

Cycling data between groups of neurons

0

1

Long Term Memory :

Change in strength of synapse connexion

Random Access Memory (RAM)

Hard Disk Drive


How Many Numbers with N-bits ?

256 128 64 32 16 8 4 2 1

0 0

1 1 from 0 to 3 are 4 numbers

What are they ?

256 128 64 32 16 8 4 2 1

0 0 0

1 1 1 from 0 to 7 are 8 numbers


Biggest Number Represented ?

256 128 64 32 16 8 4 2 1

1 1 1 1 = 15 (dec)

One less

256 128 64 32 16 8 4 2 1

1 1 1 1 1 1 1 1 = ? (dec)

One less

With 4 bits ?

With 8 bits ?


Memory Addressing

CPU

CPU

2-bit address = 4 memory cells

3-bit address = 8 memory cells

256 128 64 32 16 8 4 2 1

0 0 0 1 1 0 1 1

16 8 4 2 1

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1


Questions

So what size memory with 8 bits of address ?

So what size memory with 16 bits of address ?

… 1024 512 256 128 64 32 16 8 4 2 1


Data and Address Buses

address bus 16 bits ? Max number of memory cells ?

Memory

16 bits

CPU 8 bits

A

A

D Data bus 8 bits ? Max number which can be stored in each cell ?

D


Representing Characters - ASCII

ASCII 8bits 256 characters

Unicode 16bits 65536

ISO 36bits 17 million

ASCII (American National Standards Institute ANSI)

American Standard Code for Information Interchange

The code for H is 01001000, for e is 01100101 So the message “Hello.” can be coded as 01001000 01100101 01101100 01101100 01101111 00101110


Unicode

HEX Ascii

30 0

41 A

61 a

6D m

0D CRASCII

UNICODE

Babelmap


Adding Colored Light

All colors of light can be made from the addition of RED + GREEN + BLUE

e.g. RED + GREEN = YELLOW


Three Images Make One

RGB

(Red Green Blue)Red + Green + Blue

=


Images “IView” Applet

Zoomed areaZoom here

+

+

=

Red, green and Blue PIXELS


255

100

10

Video memory “planes”

Each PIXEL has 3 SAMPLES R G B

+

+

=

=

PIXEL SAMPLES

Cathode Ray Tube (CRT) screen


8

8

8

24 bits per pixel

255

100

10

BIU

Graphics Processor

DAC’s

CRT

memory planes


You recognize this guy. But SQUINT while looking. The image appears very much clearer. Yes!

Defocussing the image gets more information to your brain.

How? By removing distracting info produced by the sharp pixel edges


Image Processing Applet

Image Pixels Convolution KERNEL


How convolution works

0 0 0

1 2 1

0 0 0

3 6 5 4 6 4

5 0 1 0 0 0

0 1 2 0 2 1

9 4 8 4 7 7

8 7 6 8 9 7

5 7 8 9 8 7

3 6 5 4 6 4

5 0 1 0 0 0

0 1 2 0 2 1

9 4 6 4 7 7

8 7 6 8 9 7

5 7 8 9 8 7

Scan KERNEL OVER whole image, pixel by pixel and at each point do this, e.g,

(1 x 4) + (2 x 8) + (1 x 4) = 24, divide by 4 = 6

Divide = 4

input image output image


Hexadecimal Representation

We need a shorthand for representing binary numbers.

Divide a byte (8 bits) into two 4-bit nibbles.

1 1 1 0 0 1 1 0

1 1 1 0 0 1 1 0

Each nibble can be

0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1

1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1

0 1 2 3 4 5 6 7

8 9 A B C DEF

… so we have

E 6

E6


Use of Hexadecimals

2. Assembler Programming

0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1

addresses Assembler code

Yellow is FFFF00

This means

FF 255 FF 255 00 0

R G B

1. Web colours in HTML


Steganography


Sound Representation - Demo

Microcontroller loudspeaker1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0


Digital and Analogue Data

Digital

Loaf of Bread

Notes of flute

Light On or Off

Binary 0 or 1

Analogue

Glass of Water

Notes of cello

Light Dimmer

Number 2.7123..


Sound Representationrecording

Analogue from instrument162 148 96

Digital Representation

Sampled signal

playback

CBP 2005-6 Comp 1017 Digital Technologies 44Page 461

MIDI Representation

Each track stored as sequence

List of instructions to instrument how to play music.

Does not contain sounds but instructions how to make them

Midi instruments read these instructions and make the sounds represented by the instructions


The Abundance of Logic

Digital logic AND

AND in neurons

AND in programming

if (x == 2 ) && (y == 3 )) gohome

AND in language

(Holmes was a detective) AND (Holmes was on the case)


Why have we done all this ?

• Leibnitz (17th C) saw the need to make a machine to prove mathematical and logical theorems – that means could “reason” about a problem

• George Boole (19th C) produced symbolic logic (AND, NOT, NOR) which could simplify this process and capture most of “everyday reasoning” using only two states 0 and 1.

• Claude Shannon (20th C) showed how Boole’s logic could be implemented by electronic Logic GATES which were digital using only 0 or 1

• Alan Turing (20th C) showed how these problems could be solved by a simple “central processor” and a “storage tape”. This is our Computer!

• Bohme and Jacopini showed that any complex set of instructions to solve these problems could be broken down into simple programming constructs, e.g. “ if (this) then do that”

CBP 2005-6Comp 1017 Digital Technologies1. CBP 2005-6Comp 1017 Digital Technologies2.

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