## Saturday, 20 September 2014

### Analogue and Digital signals questions and solutions IB

1).        (a)        Explain what is meant by the Binary number system.
(b)        Explain why the binary number system is very important for digital electronic
systems
2)                  The table below contains both decimal and binary numbers.
Complete the table by giving the equivalent binary or decimal number.
The first row is completed for you as an example.

 Decimal Number Binary Number (a) 8 01000 (b) 4 (c) 10100 (d) 00110 (e) 15 (f) 28 (g) 11001 (h) 19

3).        (a)        Show, by calculation, that if the tape speed of a C90 Compact Cassette was
47.6mms-1    then there would be approximately 130m of tape in the cassette.

(b)        When all of the tape is spooled onto the one reel, its outer radius is 26mm and its
inner    radius is 12mm.  Estimate, by calculation, the thickness of the tape.

4).        (a)        Explain two advantages of storing information digitally.

(b)        Explain one disadvantage of storing information digitally.

5).        (a)  State three devices which can store digital information and give their approximate
capacity

(b)        A typical portable digital storage device has a capacity of 4GB.  If average size of
an    MP3 music file is 5MB, estimate, by calculation, how many music files can be
stored on   this devic

(c)        How many CDs would be required to hold the same amount of information

6).        (a)        Draw a labelled diagram to represents the vertical cross-section through a CD.

(b)        Explain briefly how information is stored on a CD.

(c)        Explain why a DVD will store more information than a CD even though they are
physically the same size.

7).        (a)        The wavelength, in air, of the light used to read a DVD is 650nm.  If the refractive
index   of the polycarbonate coating on the bottom of a DVD is 1.56, calculate the
wavelength  of the light in the polycarbonate coating.

(b)    If destructive interference is to occur with the light reflected from an island on a
DVD,calculate the height of the island.

8).      (a)        The radius of the inner track on a CD is 22mm and the outer track is 58mm.
Calculate  the area of the CD that is used for storing data.

(b)  If the spiral tracks are 1.6µm apart, estimate the length of the spiral that is used to
store     the data.

(c)   If 700MB of data is to be stored on a CD, estimate the minimum length of an island.

(d)       In practice the minimum length of a island is 830nm.  Why is this value smaller
than the   calculated value in part (c).

9).      The storage of information digitally is causing many issues including those listed below:-
Storage, Cataloguing, Moral, Ethical, Piracy, Data centres, Waste and Back up of data.

Prepare a presentation which you could deliver to local business leaders highlighting what you      consider to be the three key issues facing society associated with the digital storage of   information.

SOLUTION
The following responses are intended to act as a guide for staff and students.

1).        (a)        Base 2 number system
(b)        Enables circuits to represent numbers based on whether they are on or off,                                      corresponding to 1 and 0

2).
 Decimal Number Binary Number (a) 8 01000 (b) 4 00100 (c) 20 10100 (d) 6 00110 (e) 15 01111 (f) 28 11100 (g) 25 11001 (h) 19 10011

3).        (a)        C90 plays for 45 minutes each side = 2700s
=> 130/0.0476 = 2731s
(b)        Mean radius of tape on spool is (26 + 12) / 2 = 19mm
=> Circumference of mean radius = 2p19 = 119.38mm
=> Number of circles of tape = 130/0.11938 = 1089
Now width of tape on spool = 26 – 12 = 14mm
=> Thickness of tape = 14 / 1089 = 0.0129mm

4).        (a)        Can be easily copied for back ups, does not degrade, can be encrypted etc
(b)        Difficult to completely delete, easily copied etc

5).        (a)        Responses to this will have to adapt to technology.  Currently examples might include:-
floppy disk = 1.44MB
CD = 700MB
DVD = 4.7GB
(b)        4000 / 5 » 800 music files
(c)        4000 / 700 = 5.7 => 6CDs

6).        (a)        See support materials
(b)        On a spiral track as a series of bumps or islands (pits) representing binary numbers.
(c)        Tracks can be closer together and the islands can be smaller since they are scanned
by a   shorter wavelength laser.

7).        (a)        650 / 1.56 = 417nm
(b)        For destructive interference the path difference should be l/2, so therefore the
height of  the island should be l/4.  So island height is 417 / 4 = 104.25nm

8).      (a)        p582 - p222 = 9048mm2
(b)        Mean radius of spiral = (58 + 22) / 2 = 40mm
Circumference of mean track is 2p40 = 251.33mm
=> Area of mean track is 251.33 × 0.0016 = 0.4mm2
=> Number of circular tracks = 9048 / 0.4 = 22620
=> Taking the mean circumference total length = 22620 × 251.33 » 5.685km
(c)        700MB = 700 × 220 × 8 = 5872025600 bits.
=> 5685 / 5872025600 = 0.968µm
(d)       land region needed between the islands, error correction, block headers etc

9).      Appropriate presentation dealing with the three key issues facing society associated with
the  digital storage of information.