A bit about the computer

474 Views

Download Presentation
## A bit about the computer

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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**• 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**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**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**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**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**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**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.**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)**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**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**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**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)**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**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.**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**Example of “AND”**“Mark McGwire” AND supplement McGwire’s use of Androstenedione**Example of “OR”**“Mark McGwire” OR “Sammy Sosa” Either McGwire or Sosa or both**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**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**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.**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).**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.**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.**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.**Decimal Binary (76 1001100)**• 1 is greater than 0 so we put a 0 in the 20’s place.