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Student of the Week Slide 2 Slide 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. Slide 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. Slide 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 Slide 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 Slide 7 Introductory Video Digital TV Slide 8 Introductory Video Digital Telephones Slide 9 Binary Numbers In the decimal, or base 10, system we use the digits 1-9 and place value based on powers of 10 Slide 10 Binary Numbers In the binary, or base 2, system we use the digits 0-1 and place value based on powers of 2 Slide 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 Slide 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 Slide 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 Slide 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 Slide 15 Converting an Analogue Signal to Digital Signal Consider an analog signal that increases at a constant rate (linear relationship) Slide 16 Converting an Analogue Signal to Digital Signal If we then sample it at consistent intervals we obtain Slide 17 Converting an Analogue Signal to Digital Signal We take a reading at certain intervals and dont know what happens in between The number of samples per second is the sampling rate or sampling frequency Slide 18 Converting an Analogue Signal to Digital Signal A typical sampling rate for audio signals is 8000 times per second or once every 125 s This graph is called a pulse amplitude modulated signal The time to take a sample is very short compared to interval Slide 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 Slide 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 Slide 21 Converting an Analogue Signal to Digital Signal Division of values into specific ranges is called quantization and the levels are quantization levels Slide 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 Slide 23 Compact Disks Slide 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 Slide 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 Slide 26 Compact Disks Are The Pits Distance between paths = 1600 nm Width of a pit = 500 nm (comparable to the of green light) Pit length = 830 nm to 3560 nm Pit depth = 125 nm Slide 27 Compact Disks Are The Pits Slide 28 Bottom of the disk is coated with transparent material CDs are read by a laser from the bottom Slide 29 Compact Disks Are The Pits Slide 30 Because the laser beam cant have zero width, as the beam approaches a pit, some of the beam will be reflected off the land, some off the pit Slide 31 Compact Disks Are The Pits This produces interference The light reflected off a land travels 2d more than light reflected off a pit Slide 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 Slide 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 Slide 34 Compact Disks Are The Pits Wavelength of laser light is about 780 nm Index of refraction is 1.55 Slide 35 Compact Disks Are The Pits Pit depth is then about 126 nm Slide 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) Slide 37 Advantages of Digital Storage Read Page 461 Know advantages and disadvantages Slide 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? Slide 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? Slide 40 Slide 41 #1-19 Homework