1. REPRESENTING INFORMATION: BINARY, HEX, ASCII C ORRESPONDING R EADING : UDC C HAPTER 2 CMSC 150: Lecture 2

2. Controlling Information Watch Newman on YouTube

3. Inside the Computer: Gates AND Gate Input Wires Output Wire 0 1 0 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., 10 0 )  second place: tens (i.e., 10 1 )  third place: hundreds (i.e., 10 2 )  …  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., 2 0 )  second place: twos (i.e., 2 1 )  third place: fours (i.e., 2 2 )  …  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  8,675,309 10 = 100001000101111111101101 2  Fewer available digits in binary: more space required for representation

11. Converting Binary to Decimal  For each 1, add the corresponding power of two  1010010111101 2

12. Converting Binary to Decimal  For each 1, add the corresponding power of two  1010010111101 2 = 5309 10

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?

17. An Alternative to Binary?  100001000101111111101101 2 = 8,675,309 10  100000100101111111101101 2 = 8,544,237 10

18. An Alternative to Binary?  100001000101111111101101 2 = 8,675,309 10  100000100101111111101101 2 = 8,544,237 10

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., 16 0 )  second place: sixteens (i.e., 16 1 )  third place: two-hundred-fifty-sixes (i.e., 16 2 )  …  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)? 2 2 = 4  with three bits? 2 3 = 8  with n bits? 2 n

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 2 4 = 16 different values

26. Binary vs. Hex 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 A1010 B1011 C1100 D1101 E1110 F1111

27. Converting Binary to Hex  Moving right to left, group into bits of four  Convert each four-group to corresponding hex digit  100001000101111111101101 2

28. Converting Hex to Binary  Simply convert each hex digit to four-bit binary equivalent  BEEF 16 = 1011 1110 1110 1111 2

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. 'A' = 65 10 = ??? 2 'q' = 90 10 = ??? 2 '8' = 56 10 = ??? 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?  2 16 = 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:  01001101 2 = 77 10  01001101 2 = 'M'  01001101 10 = one million one thousand one hundred and one  You must be clear on representation and interpretation