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Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2

Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2. CMSC 150: Lecture 2 . Controlling Information. Watch Newman on YouTube. Inside the Computer: Gates. AND Gate. 0. 0. Input Wires. 1. Output Wire.

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Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2

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  1. Representing information:binary, hex, asciiCorresponding Reading:UDC Chapter 2 CMSC 150: Lecture 2

  2. Controlling Information Watch Newman on YouTube

  3. Inside the Computer: Gates AND Gate 0 0 Input Wires 1 Output Wire 0's & 1's represent low & high voltage, respectively, on the wires

  4. Inside the Computer: Gates

  5. Representing Information • We need to understand how the 0's and 1's can be used to "control information"

  6. The Decimal Number System • Deci- (ten) • Base is ten • first (rightmost) place: ones (i.e., 100) • second place: tens (i.e., 101) • third place: hundreds (i.e., 102) • … • Digits available: 0, 1, 2, …, 9 (ten total)

  7. Example: your favorite number… 8,675,309

  8. The Binary Number System • Bi- (two) • bicycle, bicentennial, biphenyl • Base two • first (rightmost) place: ones (i.e., 20) • second place: twos (i.e., 21) • third place: fours (i.e., 22) • … • Digits available: 0, 1 (two total)

  9. Representing Decimal in Binary • Moving right to left, include a "slot" for every power of two <= your decimal number • Moving left to right: • Put 1 in the slot if that power of two can be subtracted from your total remaining • Put 0 in the slot if not • Continue until all slots are filled • filling to the right with 0's as necessary

  10. Example • 8,675,30910 = 1000010001011111111011012 • Fewer available digits in binary: more space required for representation

  11. Converting Binary to Decimal • For each 1, add the corresponding power of two • 10100101111012

  12. Converting Binary to Decimal • For each 1, add the corresponding power of two • 10100101111012 = 530910

  13. Now You Get The Joke THERE ARE 10 TYPES OF PEOPLE IN THE WORLD: THOSE WHO CAN COUNT IN BINARY AND THOSE WHO CAN'T

  14. Too Much Information?

  15. Too Much Information?

  16. Too Much Information?

  17. An Alternative to Binary? • 1000010001011111111011012 = 8,675,30910 • 1000001001011111111011012 = 8,544,23710

  18. An Alternative to Binary? • 1000010001011111111011012 = 8,675,30910 • 1000001001011111111011012 = 8,544,23710

  19. An Alternative to Binary? • What if this was km to landing?

  20. The Hexadecimal Number System • Hex- (six) Deci- (ten) • Base sixteen • first (rightmost) place: ones (i.e., 160) • second place: sixteens (i.e., 161) • third place: two-hundred-fifty-sixes (i.e., 162) • … • Digits available: sixteen total 0, 1, 2, …, 9, A, B, C, D, E, F

  21. Using Hex • Can convert decimal to hex and vice-versa • process is similar, but using base 16 and 0-9, A-F • Most commonly used as a shorthand for binary • Avoid this

  22. More About Binary • How many different things can you represent using binary: • with only one slot (i.e., one bit)? • with two slots (i.e., two bits)? • with three bits? • with n bits?

  23. More About Binary • How many different things can you represent using binary: • with only one slot (i.e., one bit)? 2 • with two slots (i.e., two bits)? 22 = 4 • with three bits? 23 = 8 • with n bits? 2n

  24. Binary vs. Hex • One slot in hex can be one of 16 values 0, 1, 2, …, 9, A, B, C, D, E, F • How many bits do you need to represent one hex digit?

  25. Binary vs. Hex • One slot in hex can be one of 16 values 0, 1, 2, …, 9, A, B, C, D, E, F • How many bits do you need to represent one hex digit? • 4 bits can represent 24 = 16 different values

  26. Binary vs. Hex

  27. Converting Binary to Hex • Moving right to left, group into bits of four • Convert each four-group to corresponding hex digit • 1000010001011111111011012

  28. Converting Hex to Binary • Simply convert each hex digit to four-bit binary equivalent • BEEF16 = 1011 1110 1110 11112

  29. Representing Different Information • So far, everything has been a number • What about characters? Punctuation? • Idea: • put all the characters, punctuation in order • assign a unique number to each • done! (we know how to represent numbers)

  30. Our Idea • A: 0 • B: 1 • C: 2 • … • Z: 25 • a: 26 • b: 27 • … • z: 51 • , : 52 • . : 53 • [space] : 54 • …

  31. ASCII: American Standard Code for Information Interchange

  32. ASCII: American Standard Code for Information Interchange 'A' = 6510 = ???2 'q' = 9010 = ???2 '8' = 5610 = ???2

  33. ASCII: American Standard Code for Information Interchange 256 total characters… How many bits needed?

  34. The Problem with ASCII • What about Greek characters? Chinese? • UNICODE: use 16 bits • How many characters can we represent?

  35. The Problem with ASCII • What about Greek characters? Chinese? • UNICODE: use 16 bits • How many characters can we represent? • 216 = 65,536

  36. You Control The Information • What is this? 01001101

  37. You Control The Information • What is this? 01001101 • Depends on how you interpret it: • 010011012 = 7710 • 010011012 = 'M' • 0100110110 = one million one thousand one hundred and one • You must be clear on representation and interpretation

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