A bit about the computer Bits bytes memory
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.
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
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
Pros and Cons 4 the analog representation is fuller/richer after all there 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
Our computers are 4 digital and electronic 4 (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
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
Decimal vs. Binary 4 Decimal (base 10) – 124 = 100 + 20 + 4 – 124 = 1 102 + 2 101 + 4 100 4 Binary (base 2) – 1111100 = 64 + 32 + 16 + 8 + 4 + 0 – 1111100 = 1 26 + 1 25 + 1 24 + 1 23 + 1 22 + 0 21 + 0 20
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 (28) distinct states (which we might choose to represent the numbers 0 through 255). 4 Note computer scientists like to start counting with zero.
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)
Representing characters 4 Combinations of 0’s and 1’s be used to represent can characters 4 This is most commonly done using ASCII code 4 American Standard Code for Information Interchange
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 0011 B 01000010 J 01001010 4 4 00110100 C 01000011 K 01001011 4 5 00110101 D 0100 L 01001100 4 6 00110110 E 01000101 M 01001101 4 7 00110111 F 01000110 N 01001110
More, more 4 A kilobyte is 1, 024 (210) bytes – approx. one thousand 4 A megabyte is 1, 048, 576 (220) bytes – approx. one million 4 A gigabyte is 1, 073, 741, 824 (230) bytes – approx. one billion 4 A terabyte is 1, 099, 511, 627, 776 (240) bytes – approx. one trillion
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)
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
The Grand Total 4 N = 60 66 500 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.
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
AND 4 use to narrow searches
Example of “AND” “Mark Mc. Gwire” AND supplement Mc. Gwire’s use of Androstenedione
OR 4 use to widen searches
Example of “OR” “Mark Mc. Gwire” OR “Sammy Sosa” Either Mc. Gwire or Sosa or both
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)
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.
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=26.
Decimal Binary (76 1001100) 4 Put a 1 on the 26’s place, and subtract 64 from 76 leaving 12. 4 Ask if the next lower power of 2, 32=25 is greater than or less than or equal to what we have left (12).
Decimal Binary (76 1001100) 4 32 is greater than 12 so we put a 0 in the 25’s place. 4 16 is greater than 12 so we put a 0 in the 24’s place.
Decimal Binary (76 1001100) 4 8 is less than 12, so we put a 1 in the 23’s place, and subtract 8 from 12 leaving 4.
Decimal Binary (76 1001100) 4 4 is equal to 4, so we put a 1 in the 22’s place, and subtract 4 from 4 leaving 0. 4 2 is greater than 0 so we put a 0 in the 21’s place.
Decimal Binary (76 1001100) 4 1 is greater than 0 so we put a 0 in the 20’s place.
- Slides: 28