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Transcript of CBP 2005-6Comp 1017 Digital Technologies1. CBP 2005-6Comp 1017 Digital Technologies2.
CBP 2005-6 Comp 1017 Digital Technologies 1
CBP 2005-6 Comp 1017 Digital Technologies 2
CBP 2005-6 Comp 1017 Digital Technologies 3
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
CBP 2005-6 Comp 1017 Digital Technologies 4
… Representations
Images
Characters
234.25
Numbers
Music
electronics
CBP 2005-6 Comp 1017 Digital Technologies 5
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
CBP 2005-6 Comp 1017 Digital Technologies 6
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
CBP 2005-6 Comp 1017 Digital Technologies 7
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
CBP 2005-6 Comp 1017 Digital Technologies 8
CPU Mem I/O
Application
Functional Blocks
Transistors
CBP 2005-6 Comp 1017 Digital Technologies 9
N-MOS
in
P-MOS
in
CMOS : Complementary
Transistors
CBP 2005-6 Comp 1017 Digital Technologies 10
N-MOS
In = 0 In = 1
P-MOS
In = 1In = 0
Transistors are Switches
CBP 2005-6 Comp 1017 Digital Technologies 11
1
0
in out
Transistor Symbols
Logic Gate Symbol
Representing Electronics
CBP 2005-6 Comp 1017 Digital Technologies 12
1
0
1 0
1
0
0 1
on
off on
off
CBP 2005-6 Comp 1017 Digital Technologies 13
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
CBP 2005-6 Comp 1017 Digital Technologies 14
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
CBP 2005-6 Comp 1017 Digital Technologies 15
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
CBP 2005-6 Comp 1017 Digital Technologies 16
Combinations of Gates
3 4
bU1
Inverter
3 4
bU1
Inverter
Sum is greater than the parts
CBP 2005-6 Comp 1017 Digital Technologies 17
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
CBP 2005-6 Comp 1017 Digital Technologies 18
Investigation of Single Neurons
Microelectrode recording of Biological Neuron activation using tungsten electrode
Hubel and Weisel. Nobel Prize 1958
Photomicrograph: Height = 1mm.
CBP 2005-6 Comp 1017 Digital Technologies 19
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
CBP 2005-6 Comp 1017 Digital Technologies 20
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.
CBP 2005-6 Comp 1017 Digital Technologies 21
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
CBP 2005-6 Comp 1017 Digital Technologies 22
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
CBP 2005-6 Comp 1017 Digital Technologies 23
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
CBP 2005-6 Comp 1017 Digital Technologies 24
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 ?
CBP 2005-6 Comp 1017 Digital Technologies 25
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
CBP 2005-6 Comp 1017 Digital Technologies 26
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
CBP 2005-6 Comp 1017 Digital Technologies 27
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
CBP 2005-6 Comp 1017 Digital Technologies 28
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
CBP 2005-6 Comp 1017 Digital Technologies 29
Unicode
HEX Ascii
30 0
41 A
61 a
6D m
0D CRASCII
UNICODE
Babelmap
CBP 2005-6 Comp 1017 Digital Technologies 30
Adding Colored Light
All colors of light can be made from the addition of RED + GREEN + BLUE
e.g. RED + GREEN = YELLOW
CBP 2005-6 Comp 1017 Digital Technologies 31
Three Images Make One
RGB
(Red Green Blue)Red + Green + Blue
=
CBP 2005-6 Comp 1017 Digital Technologies 32
Images “IView” Applet
Zoomed areaZoom here
+
+
=
Red, green and Blue PIXELS
CBP 2005-6 Comp 1017 Digital Technologies 33
255
100
10
Video memory “planes”
Each PIXEL has 3 SAMPLES R G B
+
+
=
=
PIXEL SAMPLES
Cathode Ray Tube (CRT) screen
CBP 2005-6 Comp 1017 Digital Technologies 34
8
8
8
24 bits per pixel
255
100
10
BIU
Graphics Processor
DAC’s
CRT
memory planes
CBP 2005-6 Comp 1017 Digital Technologies 35
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 pro- duced by the sharp pixel edges
CBP 2005-6 Comp 1017 Digital Technologies 36
Image Processing Applet
Image Pixels Convolution KERNEL
CBP 2005-6 Comp 1017 Digital Technologies 37
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
CBP 2005-6 Comp 1017 Digital Technologies 38
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
CBP 2005-6 Comp 1017 Digital Technologies 39
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
CBP 2005-6 Comp 1017 Digital Technologies 40
Steganography
CBP 2005-6 Comp 1017 Digital Technologies 41
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
CBP 2005-6 Comp 1017 Digital Technologies 42
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..
CBP 2005-6 Comp 1017 Digital Technologies 43
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
CBP 2005-6 Comp 1017 Digital Technologies 45
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)
CBP 2005-6 Comp 1017 Digital Technologies 46
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”
