1. CBP 2005-6Comp 1017 Digital Technologies1

2. CBP 2005-6Comp 1017 Digital Technologies2

3. CBP 2005-6Comp 1017 Digital Technologies3 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

4. CBP 2005-6Comp 1017 Digital Technologies4 … Representations Images Characters 234.25 Numbers Music electronics

5. CBP 2005-6Comp 1017 Digital Technologies5 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

6. CBP 2005-6Comp 1017 Digital Technologies6 Numbers are Bits 128 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

7. CBP 2005-6Comp 1017 Digital Technologies7 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 0123456701234567

8. CBP 2005-6Comp 1017 Digital Technologies8 CPU MemI/O Application Functional Blocks Transistors

9. CBP 2005-6Comp 1017 Digital Technologies9 N-MOS in P-MOS in CMOS : Complementary Transistors

10. CBP 2005-6Comp 1017 Digital Technologies10 N-MOS In = 0 In = 1 P-MOS In = 1 In = 0 Transistors are Switches

11. CBP 2005-6Comp 1017 Digital Technologies11 1 0 in out Transistor Symbols Logic Gate Symbol Representing Electronics

12. CBP 2005-6Comp 1017 Digital Technologies12 1 0 1 0 1 0 0 1 on offon off

13. CBP 2005-6Comp 1017 Digital Technologies13 1 0 B AB A out 1 0 ABO 00 01 10 11 AND gate A B O/P X

14. CBP 2005-6Comp 1017 Digital Technologies14 Digital Logic Gates. AND gate A B O/P ABO 00 01 10 11 LOGIC SYMBOL TRUTH TABLE 0 0 0 1

15. CBP 2005-6Comp 1017 Digital Technologies15 Digital Logic Lab ABO 000 010 100 111 input switches A B O OR gate NOT gate NOR gate NAND gate

16. CBP 2005-6Comp 1017 Digital Technologies16 Combinations of Gates 34 bU1 Inverter 34 bU1 Inverter Sum is greater than the parts

17. CBP 2005-6Comp 1017 Digital Technologies17 Exercise - Find the Truth Table A B C ABCO 000 010 100 110 001 011 101 111 P 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 P O AND gate

18. CBP 2005-6Comp 1017 Digital Technologies18 Investigation of Single Neurons Microelectrode recording of Biological Neuron activation using tungsten electrode Hubel and Weisel. Nobel Prize 1958 Photomicrograph: Height = 1mm.

19. CBP 2005-6Comp 1017 Digital Technologies19 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

20. CBP 2005-6Comp 1017 Digital Technologies20 Two Gate Memory Cell 12 aU1 34 b 34 b Electronic Inverter 10 0 1 Two inverters + feedback 12 aU1 34 b 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.

21. CBP 2005-6Comp 1017 Digital Technologies21 SRAM Memory Cell 12 aU1 34 b 12 a 34 b select In/out bit 12 aU1 34 b Two inverters + feedback Neural Circuits SRAM Memory 0 1

22. CBP 2005-6Comp 1017 Digital Technologies22 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

23. CBP 2005-6Comp 1017 Digital Technologies23 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

24. CBP 2005-6Comp 1017 Digital Technologies24 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 = ? (dec) One less With 4 bits ? With 8 bits ?

25. CBP 2005-6Comp 1017 Digital Technologies25 Memory Addressing 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

26. CBP 2005-6Comp 1017 Digital Technologies26 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

27. CBP 2005-6Comp 1017 Digital Technologies27 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

28. CBP 2005-6Comp 1017 Digital Technologies28 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

29. CBP 2005-6Comp 1017 Digital Technologies29 Unicode HEXAscii 300 41A 61a 6Dm 0DCR ASCII UNICODE Babelmap

30. CBP 2005-6Comp 1017 Digital Technologies30 Adding Colored Light All colors of light can be made from the addition of RED + GREEN + BLUE e.g. RED + GREEN = YELLOW

31. CBP 2005-6Comp 1017 Digital Technologies31 Three Images Make One RGB (Red Green Blue) Red + Green + Blue=

32. CBP 2005-6Comp 1017 Digital Technologies32 Images “IView” Applet Zoomed area Zoom here + + = Red, green and Blue PIXELS

33. CBP 2005-6Comp 1017 Digital Technologies33 255 100 10 Video memory “planes” Each PIXEL has 3 SAMPLES R G B + + = = PIXELSAMPLES Cathode Ray Tube (CRT) screen

34. CBP 2005-6Comp 1017 Digital Technologies34 8 8 8 24 bits per pixel 255 100 10 BIU Graphics Processor DAC’s CRT memory planes

35. CBP 2005-6Comp 1017 Digital Technologies35 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

36. CBP 2005-6Comp 1017 Digital Technologies36 Image Processing Applet ImagePixelsConvolution KERNEL

37. CBP 2005-6Comp 1017 Digital Technologies37 How convolution works 000 121 000 365464 501000 012021 948477 876897 578987 365464 501000 012021 946477 876897 578987 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

38. CBP 2005-6Comp 1017 Digital Technologies38 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 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 0123456701234567 89ABCDEF89ABCDEF … so we have E6 E6

39. CBP 2005-6Comp 1017 Digital Technologies39 Use of Hexadecimals 2. Assembler Programming 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 addressesAssembler code Yellow is FFFF00 This means FF 255 FF 255 00 0 RGBRGB 1. Web colours in HTML

40. CBP 2005-6Comp 1017 Digital Technologies40 Steganography

41. CBP 2005-6Comp 1017 Digital Technologies41 Sound Representation - Demo Microcontrollerloudspeaker 1 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

42. CBP 2005-6Comp 1017 Digital Technologies42 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..

43. CBP 2005-6Comp 1017 Digital Technologies43 Sound Representation recording Analogue from instrument 162 148 96 Digital Representation Sampled signal playback

44. CBP 2005-6Comp 1017 Digital Technologies44 Page 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

45. CBP 2005-6Comp 1017 Digital Technologies45 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)

46. CBP 2005-6Comp 1017 Digital Technologies46 Why have we done all this ? Leibnitz (17 th C) saw the need to make a machine to prove mathematical and logical theorems – that means could “reason” about a problem George Boole (19 th 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 (20 th C) showed how Boole’s logic could be implemented by electronic Logic GATES which were digital using only 0 or 1 Alan Turing (20 th 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”