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Boolean Algebra

Boolean Algebra

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Boolean Algebra

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  1. Boolean Algebra

  2. Starter Task • State 5 basic data types together with one operation that can be performed on each. • We have looked at 4 in the past few weeks...

  3. Answers • Variable • Array • Insert a value into a certain position in the array • Stack • Pop, Push • Queue • enQueue, Serve • Binary Tree • Search through and add values / Delete values • Linked List • Add items to the list, remove items from the list

  4. Over the next Few Weeks... • Working through the booklets... • Binary Numbers • Hexadecimal Numbers • Characters • ASCII – Strings and Character sets • Negative Numbers • Two’s complement, representation sign, magnitude • Shifting • Fixed Point, Floating Point • Conversion + Benefits • Rounding + Truncation effects on accuracy • Overflow, Underflow

  5. We use Base 10... • Because we have 10 fingers

  6. What if we had 16?

  7. This gives us the structure of... • Every 10th value we add an extra number... • 2 • 12 • 23 • 178 • Etc...

  8. Base 10 looks like... • The number 1583 means 1 'thousand', 5 'hundreds', 8 'tens' and 3 'units'...

  9. Where each column is 10^X • 10^1 = 10 • 10^2 = 100 • 10^3 = 1000 • 10^4 = 10,000

  10. Consider this... • Computers only use base 2... • How would this look in a table? • What will a base 2 set of numbers look like?

  11. Base 2

  12. Base 2

  13. Representing numbers... • What number do you think this will represent? • 10010110

  14. Base 2

  15. 150

  16. What do the following numbers = • 10000101 • 01000001 • 11111111 • 10110101 • 00000000 • 10101111 • 00101010 • 00111011 • 10111010

  17. Answers • 10000101 = 128 + 0 + 0 + 0 + 0 + 4 + 0 + 1 = 133 • 65 • 255 • 181 • 0 • 175 • 42 • 59 • 186

  18. What if I wanted to go the other way... • How would I convert 22 into binary?

  19. Actions • 22 / 2 = 11 r 0 • _ _ _ _0

  20. Actions • 22 / 2 = 11 r 0 • 11 / 2 = 5 r 1 • _ _ _10

  21. Actions • 22 / 2 = 11 r 0 • 11 / 2 = 5 r 1 • 5 / 2 = 2 r 1 • _ _110

  22. Actions • 22 / 2 = 11 r 0 • 11 / 2 = 5 r 1 • 5 / 2 = 2 r 1 • 2 / 2 = 1 r 0 • _ 0110

  23. Actions • 22 / 2 = 11 r 0 • 11 / 2 = 5 r 1 • 5 / 2 = 2 r 1 • 2 / 2 = 1 r 0 • 1 / 2 = 0 R 1 • 1 0110

  24. What if I wanted to go the other way... • How would I convert 22 into binary?

  25. Actions • Divide each value into largest number and put a one in the table...

  26. What are the following binary numbers? • 156 • 45 • 78 • 97 • 123 • 245 • 253 • 7 • 184 • 111

  27. What are the following binary numbers? • 156 = 10011100 • 45 = 00101101 • 78 = 01001110 • 97 = 01100001 • 123 = 01111011 • 245 = 11110101 • 253 = 11111101 • 7 = 00000111 • 184 = 10111000 • 111 = 01101111

  28. Bytes • So far everything has consisted of once byte... • 8 bits... Byte • 4bits... Nybble (rarely used now) • 1101=13

  29. Standard Computers are 32bit... • What would be the maximum value that a 32bit computer can hold? • You might want to use a calculator...

  30. 32 bit = 4,294,967,295 • This is the biggest value for a 32bit computer... • However it doesn’t exist in many operating systems...

  31. 64Bit... • What about 64bit?

  32. Again... • 18,446,744,073,709,552,000 • This number will not be found in 64bit operating systems... • Can you look down the list of contents in the booklet to see why?

  33. Summary Video’s • http://www.youtube.com/watch?v=qdFmSlFojIw • http://courses.cs.vt.edu/csonline/NumberSystems/Lessons/DecimalToBinaryConversion/index.html

  34. Convertor • http://mistupid.com/computers/binaryconv.htm

  35. Lesson 2 • Hexadecimal notation... • What do you think hexadecimal notation looks like?

  36. Hexadecimal notation

  37. What’s it used for • Give a more readable notation for people to use. • Decimal = 10,995 • Binary = 10101011110011 • Hexadecimal = 2AF3 

  38. How it’s used... • Have you ever seen... • #33FD56 • In HTML coding... • Gives you a colour • #33FD56

  39. Each part = nybble • #33FD56 • 33 = 51 =0011 0011 • FD = 253 =1111 1101 • 56 = 86 =0101 0110

  40. Task 2 • Fill in the table: You will have to remember how to complete binary numbers...

  41. Now we have 3 ways to represent numbers... • What is the point? • We can represent 0-255 numbers using 1byte or 1 hexadecimal code • Can you think of why we would use this?

  42. Character Sets • All the symbols, letters, numbers have a binary representation • There are 128 different characters that we call ASCII This is a Standard!

  43. ASCII • (American Standardised Code for Information Interchange) • Needed so that computers share documents together: Others include: EBCDIC(Extended Binary Coded Decimal Interchange Code) ISO 8859, for ß (German), ñ (Spanish), å (Swedish) ANSI (American National Standards Institute)

  44. ASCII Character Set

  45. Words • In order to write the word Hello

  46. Task • How would hello world read? • How many bits are used for each character?

  47. Hello World • 01001000 01100101 01101100 01101100 01101111 00100000 01010111 01101111 01110010 01101100 01100100

  48. Hello World • 48 65 6c 6c 6f 20 57 6f 72 6c 64

  49. Practice • What about the sentence: • There are 10 types of people in the world: those who understand binary, and those who don't.