A bit about the computer

1. 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.

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

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

4. Pros and Cons • the analog representation is fuller/richer after all there are an infinite number of values available • 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

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

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

7. Decimal vs. Binary • Decimal (base 10) • 124 = 100 + 20 + 4 • 124 = 1  102 + 2  101 + 4  100 • Binary (base 2) • 1111100 = 64 + 32 + 16 + 8 + 4 + 0 + 0 • 1111100 = 1  26 + 1  25 + 1  24 + 1  23 + 1  22 + 0  21 + 0  20

8. Bits and Bytes • A bit is a single binary digit (0 or 1). • A byte is a group of eight bits. • A byte can be in 256 (28) distinct states (which we might choose to represent the numbers 0 through 255). • Note computer scientists like to start counting with zero.

9. Realizing a bit • 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)

10. Representing characters • Combinations of 0’s and 1’s can be used to represent characters • This is most commonly done using ASCII code • American Standard Code for InformationInterchange

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

12. More, more, more • Akilobyte is 1,024 (210) bytes • approx. one thousand • A megabyte is 1,048,576 (220) bytes • approx. one million • Agigabyte is 1,073,741,824 (230) bytes • approx. one billion • A terabyte is 1,099,511,627,776 (240) bytes • approx. one trillion

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

14. Storing the Starr report • The report plus supporting material • 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

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

16. True or False • A boolean expression is a condition that is either true or false (on or off) • 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

17. use to narrow searches AND

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

19. use to widen searches OR

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

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

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

23. Decimal  Binary • Take the decimal number 76 • Look for the largest power of 2 that is less than 76. • The powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, etc. • So the largest power of 2 less than 76 is 64=26.

24. Decimal  Binary (76  1001100) • Put a 1 on the 26’s place, and subtract 64 from 76 leaving 12. • Ask if the next lower power of 2, 32=25 is greater than or less than or equal to what we have left (12).

25. Decimal  Binary (76  1001100) • 32 is greater than 12 so we put a 0 in the 25’s place. • 16 is greater than 12 so we put a 0 in the 24’s place.

26. Decimal  Binary (76  1001100) • 8 is less than 12, so we put a 1 in the 23’s place, and subtract 8 from 12 leaving 4.

27. Decimal  Binary (76  1001100) • 4 is equal to 4, so we put a 1 in the 22’s place, and subtract 4 from 4 leaving 0. • 2 is greater than 0 so we put a 0 in the 21’s place.

28. Decimal  Binary (76  1001100) • 1 is greater than 0 so we put a 0 in the 20’s place.