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1 REPRESENTING INFORMATION: BINARY, HEX, ASCII CORRESPONDING READING: WELL, NONE IN YOUR TEXT. SO LISTEN CAREFULLY IN LECTURE (BECAUSE IT WILL BE ON THE EXAM(S))! CMSC 150: Fall 2015

2 Controlling Information Watch Newman on YouTube

3 Inside the Computer: Gates AND Gate Input Wires 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., 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 Phrase binary digit shortened to bit

9 Quantity of Bits (Memory) 9 1 Byte (1B) = 8 bits 1 Kilobyte (1KB) = 2 10 = 1024 bytes 1 Megabyte (1MB) = 2 20 ~ 1,000,000 bytes 1 Gigabyte (1GB) = 2 30 ~ 1,000,000,000 bytes 1 Terabyte (1TB) = 2 40 ~ 1,000,000,000,000 bytes These last four have beens standardized of late for powers of 10, rather than 2 (e.g., 10 3, 10 6, 10 9, )

10 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 n filling to the right with 0's as necessary

11 Example 8,675, = Fewer available digits in binary: more space required for representation

12 Converting Binary to Decimal For each 1, add the corresponding power of two

13 Converting Binary to Decimal For each 1, add the corresponding power of two =

14 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

15 Too Much Information?

16 Too Much Information?

17 Too Much Information?

18 An Alternative to Binary? = 8,675, = 8,544,237 10

19 An Alternative to Binary? = 8,675, = 8,544,237 10

20 An Alternative to Binary? What if this was km to landing?

21 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

22 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

23 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?

24 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

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?

26 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

27 Binary vs. Hex A 1010 B 1011 C 1100 D 1101 E 1110 F 1111

28 Converting Binary to Hex Moving right to left, group into bits of four Convert each four-group to corresponding hex digit

29 Converting Hex to Binary Simply convert each hex digit to four-bit binary equivalent BEEF 16 =

30 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)

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

32 ASCII: American Standard Code for Information Interchange

33 ASCII: American Standard Code for Information Interchange 'A' = =??? 2 'q' = =??? 2 '8' = =??? 2

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

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

36 The Problem with ASCII What about Greek characters? Chinese? UNICODE: use 16 bits How many characters can we represent? 2 16 = 65,536

37 You Control The Information What is this?

38 You Control The Information What is this? Depends on how you interpret it: = = 'M' = one million one thousand one hundred and one You must be clear on representation and interpretation

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