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Chaos, Communication and Consciousness Module PH19510

Chaos, Communication and Consciousness Module PH19510. Lecture 9 Codes. 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. Braille.

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Chaos, Communication and Consciousness Module PH19510

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  1. Chaos, Communication and ConsciousnessModule PH19510 Lecture 9 Codes

  2. 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

  3. Braille Semaphore Morse ASCII A=1000001, F=1000110, K=1001011 B=1000010, G=1000111, L=1001100 C=1000011, H=1001000, M=1001101 D=1000100, I=1001001, N=1001110 E=1000101, J=1001010, O=1001111 Codes • Represent information into form for: • transmission • storage • processing • Alphabet • Numbers

  4. Evolution of Alphabets • Ideographs • 1 symbol / idea • Hieroglyphs • 1 symbol / syllable • Alphabet • Syllables encoded in alphabet abcdefghijlkmnopqrstuvwxyz ABCDEFGHIJLKMNOPQRSTUVWXYZ

  5. 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

  6. 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

  7. Analogue & Digital Information • Analogue Information • Any value between limits • Most ‘real world’ quantities are analogue • Temperature, pressure, light intensity etc • Digital Information • Only discrete values possible • Numbers, Letters, other abstractions

  8. 1 0 Why Binary ? • Noise is endemic in circuits • Freedom from noise •  process information faithfully Input Device Output Device 1 Noise Margin 0

  9. George Boole (1815 – 1864) • Mathematician • Symbolic Methods • 1847 “Mathematical analysis of Logic” • Analogy between algebra & logic • Symbolic operations on logical propositions • Equations in logic • Boolean algebra

  10. 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

  11. 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

  12. 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 Binary Counting

  13. 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 = 220bytes Gigabyte GB 1,073,741,824 =230 bytes Terabyte TB 1,099,511,627,776 =240 bytes Powers of 2

  14. Rotary Shaft Encoder Gray code • Re-arrange binary counting • Only 1 bit changes at a time • Rotary encoders

  15. Jean-Maurice-Émile Baudot • 1874 Multiplexing printing telegraph system • Up to 4 telegraph channels on single wire • Time Division Multiplexing • 5 bit code

  16. Baudot code

  17. 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

  18. Pulse code Modulation (PCM) • Sample analogue signal • n-bits • 2n levels • Quantisation Noise Quantisation Noise

  19. 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

  20. 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

  21. 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

  22. 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)

  23. 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

  24. Error Correcting Codes • Put extra information in data stream to detect and correct errors • Hamming Codes • Reed-Solomon

  25. 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

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