1. Student of the Week

3. Assessment Statements IB Topic 14.1., Analogue and Digital Signals 14.1.1.Solve problems involving the conversion between binary numbers and decimal numbers. 14.1.2.Describe different means of storage of information in both analogue and digital forms. 14.1.3.Explain how interference of light is used to recover information stored on a CD.

4. Assessment Statements IB Topic 14.1., Analogue and Digital Signals 14.1.4.Calculate an appropriate depth for a pit from the wavelength of the laser light. 14.1.5.Solve problems on CDs and DVDs related to data storage capacity. 14.1.6.Discuss the advantage of the storage of information in digital rather than analogue form.

5. Objectives  Convert decimal numbers into binary numbers and vice versa  Understand the difference between an analogue signal and a digital signal  Convert an analogue signal into a digital signal  Outline the structure of a compact disc  Appreciate the role of interference in reading a CD

6. Objectives  Calculate pit depths in terms of the wavelength of light used  Outline the basic structure of various storage devices  Outline the advantages of digital storage

7. Introductory Video – Digital TV

8. Introductory Video – Digital Telephones

9. Binary Numbers  In the decimal, or base 10, system we use the digits 1-9 and place value based on powers of 10

10. Binary Numbers  In the binary, or base 2, system we use the digits 0-1 and place value based on powers of 2

11. Binary Numbers  In the binary system, each place value is called a bit  10101 has five digits so it is a 5-bit word  The number of values is limited by the number of bits  5-bit numbers have 2 5 values = 32 values  A 16-bit word has 65,536 possible values  A 32-bit word has 4,294,967,296 possible values  Newer systems are 64-bit which has a whole bunch of values

12. Binary Numbers  In a binary number, the first non-zero digit (left side) is the most significant bit (MSB)  The last digit is the least significant bit (LSB)  In the binary number 011101,  The first 1 (2 4 ) is the most significant bit and  The last 0 (2 0 ) is the least significant bit

13. Analogue Signal  Analogue signals are continuous signals, varying between two Extreme values in a way that is proportional to the physical mechanism that created the signal.  A mercury thermometer gives a continuous measurement of temperature  A microphone produces a continuous voltage signal based on the vibrations of a diaphragm

14. Digital Signal  Digital signals are coded forms of a signal that takes discrete values of 0 or 1 only.  The LabQuest with a temperature probe is programmed to take x number of samples per second and is idle between measurements

15. Converting an Analogue Signal to Digital Signal  Consider an analog signal that increases at a constant rate (linear relationship)

16. Converting an Analogue Signal to Digital Signal  If we then sample it at consistent intervals we obtain

17. Converting an Analogue Signal to Digital Signal  We take a reading at certain intervals and don’t ‘know’ what happens in between  The number of samples per second is the sampling rate or sampling frequency

18. Converting an Analogue Signal to Digital Signal  A typical sampling rate for audio signals is 8000 times per second or once every 125 μs  This graph is called a pulse amplitude modulated signal  The time to take a sample is very short compared to interval

19. Converting an Analogue Signal to Digital Signal  We now convert the signal sampling into a binary code using 2-bit words  2 2 means we can have 4 distinct values  In a sense, this is like rounding the signal to significant parts

20. Converting an Analogue Signal to Digital Signal  We can decrease the amount of ‘lost’ information by using 3-bit words  2 3 means we can have 8 distinct values  Increased intervals / values means increased fidelity

21. Converting an Analogue Signal to Digital Signal  Division of values into specific ranges is called quantization and the levels are quantization levels

22. Converting an Analogue Signal to Digital Signal  This gives rise to quantization error  For the 2-bit data the error is 2V  For the 3-bit data the error is 1V

23. Compact Disks

24. Compact Disks Are The Pits  Analogue data is converted to digital if required  Digital data is then imprinted on the CD by a series of marks called pits  The edge of a pit corresponds to a binary ‘1’

25. Compact Disks Are The Pits  The ‘unpitted’ part is called a land.  A series of pits are made along a path that spirals from the center outward

26. Compact Disks Are The Pits  Distance between paths = 1600 nm  Width of a pit = 500 nm (comparable to the λ of green light)  Pit length = 830 nm to 3560 nm  Pit depth = 125 nm

27. Compact Disks Are The Pits

28.  Bottom of the disk is coated with transparent material  CD’s are read by a laser from the bottom

29. Compact Disks Are The Pits

30.  Because the laser beam can’t have zero width, as the beam approaches a pit, some of the beam will be reflected off the land, some off the pit

31. Compact Disks Are The Pits  This produces interference  The light reflected off a land travels 2d more than light reflected off a pit

32. Compact Disks Are The Pits  The light reflected off a land travels 2d more than light reflected off a pit  If we choose 2d to be half a wavelength

33. Compact Disks Are The Pits  If we choose 2d to be half a wavelength, the interference between the two reflections will be destructive and the reflected light will have zero intensity

34. Compact Disks Are The Pits  Wavelength of laser light is about 780 nm  Index of refraction is 1.55

35. Compact Disks Are The Pits  Pit depth is then about 126 nm

36. Other Storage Devices  DVDs  LPs  Cassettes  Floppy Discs  Hard Discs  Read Pages 459-461 to know the advantages and disadvantages of each of these (this is eerily like the advantages and disadvantages of different energy sources)

37. Advantages of Digital Storage  Read Page 461  Know advantages and disadvantages

38. Summary  Can you convert decimal numbers into binary numbers and vice versa?  Do you understand the difference between an analogue signal and a digital signal?  Can you convert an analogue signal into a digital signal?  Can you outline the structure of a compact disc?  Do you appreciate the role of interference in reading a CD?

39. Summary  Can you calculate pit depths in terms of the wavelength of light used?  Can you outline the basic structure of various storage devices?  Can you outline the advantages of digital storage?

41. #1-19 Homework