2. A bit about the computer Bits, bytes, memory and so on Some of this material can be found in Discovering Computers 2000 (Shelly, Cashman and Vermaat) 3.11-3.13 and the appendix A.1-A.4.

3. A computer is 4 a person or thing that computes 4 to compute is to determine by arithmetic means (The Randomhouse Dictionary) 4 so computing involves numbers 4 While typing papers, drawing pictures and surfing the Net don’t seem to involve numbers at first, numbers are lurking beneath the surface

4. Representing numbers 4 Some attribute of the computer is used to “represent” numbers (for example: a child’s fingers) 4 two kinds of representation are: –analog the numbers represented take on a continuous set of values –digital the numbers represented take on a discrete set of values

5. Pros and Cons 4 the analog representation is fuller/richer after all there are an infinite number of values available 4 the digital representation is safer from corruption by “noise;” there is a big difference between the various discrete values, and smaller, more subtle differences do not affect the representation

6. Our computers are 4 digital and electronic  (note that digital  electronic) 4 they are electronic because they use an electronic means (e.g. voltage or current) to represent numbers 4 they are digital because the numbers represented are discrete

7. Binary representation 4 the easiest distinction to make is between –low and high voltage –off and on 4 then we can only represent two digits: 0 and 1 4 but we can represent any (whole) number using 0’s and 1’s

8. Decimal vs. Binary 4 Decimal (base 10) –124 = 100 + 20 + 4 –124 = 1  10 2 + 2  10 1 + 4  10 0 4 Binary (base 2) –1111100 = 64 + 32 + 16 + 8 + 4 + 0 + 0 –1111100 = 1  2 6 + 1  2 5 + 1  2 4 + 1  2 3 + 1  2 2 + 0  2 1 + 0  2 0

9. Bits and Bytes 4 A bit is a single binary digit (0 or 1). 4 A byte is a group of eight bits. 4 A byte can be in 256 (2 8 ) distinct states (which we might choose to represent the numbers 0 through 255). 4 Note computer scientists like to start counting with zero.

10. Realizing a bit 4 We need two “states,” e.g. –high or low voltage (e.g. computer chips) why you should protect computer from power surges –north or south pole of a magnet (e.g. floppy disks) why you should keep floppies away from large magnets –light or dark (e.g. CD) –hole or no hole (e.g. punch card or CD)

11. Representing characters 4 Combinations of 0’s and 1’s can be used to represent characters 4 This is most commonly done using ASCII code 4 A merican S tandard C ode for I nformation I nterchange

12. ASCII code (a byte per character) 4 0 00110000 8 00111000 G 01000111 4 1 00110001 9 00111001 H 01001000 4 2 00110010 A 01000001 I 01001001 4 3 00110011 B 01000010 J 01001010 4 4 00110100 C 01000011 K 01001011 4 5 00110101 D 01000100 L 01001100 4 6 00110110 E 01000101 M 01001101 4 7 00110111 F 01000110 N 01001110

13. More, more, more 4 A kilobyte is 1,024 (2 10 ) bytes –approx. one thousand 4 A megabyte is 1,048,576 (2 20 ) bytes –approx. one million 4 A gigabyte is 1,073,741,824 (2 30 ) bytes –approx. one billion 4 A terabyte is 1,099,511,627,776 (2 40 ) bytes –approx. one trillion

14. Storing it away 4 A standard 3.5 inch floppy disk holds 1.44 MB (megabytes) 4 An Iomega Zip disk holds approx. 100 MB –(the computers in Olney 200 have zip drives) 4 A CD holds approx. 600 MB 4 A typical hard drive holds a few GB (gigabytes)

15. Storing the Starr report 4 The report plus supporting material 4 If there were: –60 characters per line –66 lines per page (single spaced) –500 pages in a ream of paper –10 reams in a box –and 18 boxes

16. The Grand Total 4 N = 60  66  500  10  18 4 N = 356,400,000 4 N  340 MB (megabytes) 4 The Starr report and the accompanying materials would fit on a few zip disks or one writable CD.

17. True or False 4 A boolean expression is a condition that is either true or false (on or off) 4 Logical operators: –like an arithmetic operator (e.g. addition) that takes in two numbers (operands) and yields a number as a result (1+1=2) –Logical operators take in two boolean expressions and produces a boolean outcome

18. AND 4 use to narrow searches

19. Example of “AND” “Mark McGwire” AND supplement McGwire’s use of Androstenedione

20. OR 4 use to widen searches

21. Example of “OR” “Mark McGwire” OR “Sammy Sosa” Either McGwire or Sosa or both

22. Transistors 4 When bits are represented using voltage, the logical operators (gates) can be constructed from transistors 4 The Pentium ® II has approximately 7.5 million transistors on it 4 The transistors have lengths approximately 0.35 microns (millionths of a meter)

23. Extra slides 4 The following slides are on converting numbers from decimal to binary 4 Don’t panic. I never ask this on tests. 4 I just like to expose people to it.

24. Decimal  Binary 4 Take the decimal number 76 4 Look for the largest power of 2 that is less than 76. 4 The powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, etc. 4 So the largest power of 2 less than 76 is 64=2 6.

25. Decimal  Binary (76  1001100) 4 Put a 1 on the 2 6 ’s place, and subtract 64 from 76 leaving 12. 4 Ask if the next lower power of 2, 32=2 5 is greater than or less than or equal to what we have left (12).

26. Decimal  Binary (76  1001100) 4 32 is greater than 12 so we put a 0 in the 2 5 ’s place. 4 16 is greater than 12 so we put a 0 in the 2 4 ’s place.

27. Decimal  Binary (76  1001100) 4 8 is less than 12, so we put a 1 in the 2 3 ’s place, and subtract 8 from 12 leaving 4.

28. Decimal  Binary (76  1001100) 4 4 is equal to 4, so we put a 1 in the 2 2 ’s place, and subtract 4 from 4 leaving 0. 4 2 is greater than 0 so we put a 0 in the 2 1 ’s place.

29. Decimal  Binary (76  1001100) 4 1 is greater than 0 so we put a 0 in the 2 0 ’s place.