Chaos, Communication and Consciousness Module PH19510 Lecture 9 Codes.

Chaos, Communication and ConsciousnessModule PH19510

Lecture 9Codes

Overview of Lecture

What is a code ? Analogue & Digital Information Information Pioneers - Boole & Shannon The bit and binary signals Baudot & ASCII codes PCM Encoding Error Detection & Correction

Codes

Represent information into form for: transmission storage processing

Alphabet Numbers

Braille

Semaphore

Morse

A=1000001, F=1000110, K=1001011B=1000010, G=1000111, L=1001100C=1000011, H=1001000, M=1001101D=1000100, I=1001001, N=1001110E=1000101, J=1001010, O=1001111

ASCII

Evolution of Alphabets

Ideographs 1 symbol / idea

Hieroglyphs 1 symbol / syllable

Alphabet Syllables encoded in

alphabet abcdefghijlkmnopqrstuvwxyzABCDEFGHIJLKMNOPQRSTUVWXYZ

Evolution of Numbers

Tally Marks

Mesopotamian Sexagesimal

Roman numerals

Arabic numerals

I II III IV V VIVII VIII IX X

0 1 2 3 4 5 6 7 8 9

Nature’s Code

Genetic information is stored in a code based on 4 units - adenine (A), thymine (T), guanine (G) and cytosine (C)

4-character code is stored on DNA, whose structure was discovered by Crick and Watson in 1953

Bacterium 600,000 pairs Human 3 x 109 pairs

Analogue & Digital Information

Analogue InformationAny value between limitsMost ‘real world’ quantities are analogueTemperature, pressure, light intensity etc

Digital InformationOnly discrete values possibleNumbers, Letters, other abstractions

Noise Margin

Why Binary ?

Noise is endemic in circuits Freedom from noise process information faithfully

0

1Output Device

0

1

Input Device

George Boole (1815 – 1864)

Mathematician Symbolic Methods 1847 “Mathematical analysis of Logic”

Analogy between algebra & logicSymbolic operations on logical propositionsEquations in logic

Boolean algebra

Claude Shannon (1916-2001)

1937 “A Symbolic Analysis of Relay and Switching Circuits” Applied Boolean algebra to relay circuits Relays can solve problems in Boolean algebra

1948 “A Mathematical Theory of Communication” Best way to encode information for transmission Maximise transmission in presence of noise

The Bit

Binary Digit Fundamental unit of

information System has N different

states (equally likely) requires n bits to transmit

information on state If states are not equally

likely, less information

)2ln(

)ln(Nn

Binary Counting

0 - 0 1 - 1 2 - 10 3 - 11 4 - 100 5 - 101 6 - 110 7 - 111 8 – 1000 …

4210 = 101010B=1x32+0x16+1x8+0x4+1x2+0x1

Streams of 1s and 0s cumbersome Break into groups of 4 bits 4 bits = 0 – 15 ==

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Hexadecimal 4210 = 2A Hex

Powers of 2

Group bits for convenience 4 bits = nibble 8 bits = byte 16 bits = word 32 bits = double word 64 bits = quad word

Kilobyte kB 1024 = 210 bytes

Megabyte MB 1,048,576 = 220 bytes

Gigabyte GB 1,073,741,824 =230 bytes

Terabyte TB 1,099,511,627,776 =240 bytes

Gray code

Re-arrange binary counting

Only 1 bit changes at a time

Rotary encoders

Position Code

0 0000

1 0001

2 0011

3 0010

4 0110

5 0111

6 0101

7 0100

8 1100

9 1101

10 1111

11 1110

12 1010

13 1011

14 1001

15 1000

Rotary Shaft Encoder

Jean-Maurice-Émile Baudot

1874 Multiplexing printing telegraph system

Up to 4 telegraph channels on single wire

Time Division Multiplexing

5 bit code

Baudot codeBin Hex Dec LTRS FIGS Bin Hex Dec LTRS FIGS

00011 03 3 A - 10111 17 23 Q 1

11001 19 25 B ? 01010 0A 10 R 4

01110 0E 14 C : 00101 05 5 S '

01001 09 9 D $ 10000 10 16 T 5

00001 01 1 E 3 00111 07 7 U 7

01101 0D 13 F ! 11110 1E 30 V ;

11010 1A 26 G & 10011 13 19 W 2

10100 14 20 H # 11101 1D 29 X /

00110 06 6 I 8 10101 15 21 Y 6

01011 0B 11 J <BELL> 10001 11 17 Z "

01111 0F 15 K ( 01000 08 8 <CR> <CR>

10010 12 18 L ) 00010 02 2 <LF> <LF>

11100 1C 28 M . 00100 04 4 <SP> <SP>

01100 0C 12 N , 11111 1F 31 <LTRS> <LTRS>

11000 18 24 O 9 11011 1B 27 <FIGS> <FIGS>

10110 16 22 P 0 00000 00 0 [..unused..]

ASCIIAmerican Standard Code for Information Interchange

Published 1967 7-bit code 128 characters 95 Printable characters 33 Non-Printing controls

STX,ETX,EOT,BEL,NUL…

8-bit extensions Code page upper 128

Pulse code Modulation (PCM)

Sample analogue signal

n-bits 2n levels Quantisation

Noise

Quantisation Noise

Sampling Frequency and Aliasing Distortion Need to sample signal

‘often’ enough Example signal: Sample 1

Frequency high enough

Sample 2 Sampling just high enough

Sample 3 Sampling to slow Aliasing Distortion

0 0.2 0.4 0.6 0.8

1

0

1

Signal

0 0.2 0.4 0.6 0.8

1

0

1

SignalSampled

0 0.2 0.4 0.6 0.8

1

0

1

SignalSampled

0 0.2 0.4 0.6 0.8

1

0

1

SignalSampled

Nyquist Criterion

Sampling Frequency must be at least twice the highest frequency in the signal

fSample 2 x fSignal

Filter signal to remove high frequencies

Wagon wheel (temporal) Patterned clothing on TV (spatial) Photocopying/scanning banknotes

PCM Audio Sampling

Rate and number of levels dependent on quality

fsample = 2 x fsignal Speech 8-bit (256 levels) 8kHz CD quality 16-bit (65,536 levels) 44kHz

Redundant Information

English text has redundant information Wasteful of space but… Allows recovery from errors If yu cn rd ths yu cn gt a gd jb prgrmmng cmptrs

Error Detecting Codes (EDC) Error correcting codes (ECC)

Error Detecting Codes

Add redundant information to detect errors Parity

Add extra bit to each ‘byte’ of information Calculate bit so always odd number of bits Can detect single bit errors

Checksums (CRC – Cyclic Redundancy check) Complex polynomial based on all bits of message Can detect errors & transpositions Information storage & transmission Credit Cards DVLA Driver numbers

Error Correcting Codes

Put extra information in data stream to detect and correct errors

Hamming Codes Reed-Solomon

Review of Lecture

What is a code ? Analogue & Digital Information Information Pioneers - Boole & Shannon The bit and binary signals Baudot & ASCII codes PCM Encoding Error Detection & Correction