Download presentation

Presentation is loading. Please wait.

Published byAli Stukes Modified about 1 year ago

1
CMSC 150 DATA REPRESENTATION CS 150: Mon 30 Jan 2012

2
What Happens When… 2

3
Steps Of An Executing Program 3 Initially, the program resides as a (binary) file on the disk

4
4 Steps Of An Executing Program When you click an icon to start a program…

5
5 Steps Of An Executing Program the program is copied from disk into memory (RAM)… the program is copied from disk into memory (RAM)…

6
6 Steps Of An Executing Program so the program can be executed by the CPU…

7
… … A Program in Memory Program: consists of instructions & data Instructions & data stored together in memory

8
… … Instructions A Program in Memory

9
… … A Program in Memory Instructions Data

10
… … A Program in Memory Instructions Data How do we interpret these 0's and 1's?

11
The Decimal Number System Deci- 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)

12
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)

13
Lingo Bit (b): one binary digit (0 or 1) Byte (B): eight bits Prefixes: Kilo (K)= 2 10 = 1024 Mega (M)= 2 20 = 1,048,576 = 2 10 K Giga (G)= 2 30 = 1,073,741,824 = 2 10 M Tera (T)= 2 40 = 1,099,511,627,776 = 2 10 G Peta (P)= 2 50 = 1,125,899,906,842,624 = 2 10 T … Yotta (Y)= 2 80 = 1,208,925,819,614,629,174,706,176 = 2 30 P

14
Representing Decimal in Binary Moving right to left, include a "slot" for every power of two ≤ your decimal number Then, 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

15
Example: A Famous Number Anyone recognize this number ?

16
Example: A Famous Number Anyone recognize this number ? 8,675, = ????????????????????? 2 What is 2 10 ?

17
Example: A Famous Number Anyone recognize this number ? 8,675, = ????????????????????? 2 What is 2 10 ? 2 20 ?

18
Example: A Famous Number Anyone recognize this number ? 8,675, = ????????????????????? 2 What is 2 10 ? 2 20 ? 2 30 ?

19
Example: A Famous Number Anyone recognize this number ? 8,675, = ????????????????????? 2 What is 2 10 ? 2 20 ? 2 30 ? 2 25 ?

20
Example: A Famous Number Anyone recognize this number ? 8,675, = ????????????????????? 2 What is 2 10 ? 2 20 ? 2 30 ? 2 25 ? Need 24 places (bits) 2 23 = 8,388,608

21
To the whiteboard, Robin !

22
Example: A Famous Number Anyone recognize this number ? 8,675, = Fewer available digits in binary more space required for representation

23
Converting Binary to Decimal For each 1, add the corresponding power of two

24
Converting Binary to Decimal For each 1, add the corresponding power of two =

25
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

26
Why Binary? ABA xor BA and B Circuits: low voltage == 0, high voltage == 1

27
Why Binary? ABA xor BA and B Circuits: low voltage == 0, high voltage == 1

28
Why Binary? ABA xor BA and B A + B sum A + B carry Circuits: low voltage == 0, high voltage == 1 Half Adder

29
An Alternative to Binary? = 8,675, = 8,544,237 10

30
An Alternative to Binary? = 8,675, = 8,544, What if this was km to landing?

31
The Hexadecimal Number System Hexa- (six) Decimal (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

32
Wikipedia says… Donald Knuth has pointed out that the etymologically correct term is "senidenary", from the Latin term for "grouped by 16". The terms "binary", "ternary" and "quaternary" are from the same Latin construction, and the etymologically correct term for "decimal" arithmetic is "denary". Schwartzman notes that the pure expectation from the form of usual Latin-type phrasing would be "sexadecimal", but then computer hackers would be tempted to shorten the word to "sex".

33
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

34
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?

35
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

36
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 to represent one hex digit? I.e., how many bits to represent 16 different things?

37
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 to represent one hex digit? 4 bits can represent 2 4 = 16 different values

38
Binary vs. Hex A1010 B1011 C1100 D1101 E1110 F1111

39
Converting Binary to Hex Moving right to left, group into bits of four Convert each four-group to corresponding hex digit

40
Converting Binary to Hex Moving right to left, group into bits of four Convert each four-group to corresponding hex digit

41
Converting Binary to Hex Moving right to left, group into bits of four Convert each four-group to corresponding hex digit F E D = 845FED 16

42
Converting Hex to Binary Convert each hex digit to four-bit binary equivalent BEEF 16 = ???? 2

43
Converting Hex to Binary Convert each hex digit to four-bit binary equivalent BEEF 16 =

44
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)

45
ASCII: American Standard Code for Information Interchange

46
'A' = = 'c' = = '8' = = ASCII: American Standard Code for Information Interchange

47
256 total characters… How many bits needed? ASCII: American Standard Code for Information Interchange

48
The Problem with ASCII What about Greek characters? Chinese? UNICODE: use more bits UTF-8: use 1-4 eight-bit bytes 1,112,064 “code points” backward compatible w/ ASCII How many characters could we represent w/ 32 bits? 2 32 = 4,294,967,296

49
You Control The Information What is this?

50
You Control The Information What is this? Depends on how you interpret it: = = 'M' = one million one thousand one hundred & one A machine-language instruction You must be clear on representation and interpretation

51
Strings… "1000" There are four characters '1' '0' '0' '0' The binary representation is =

52
Strings… "1000" There are four characters '1' '0' '0' '0' The binary representation is = “1234” ≠ 1234

53
One Last Thing… Real valued (AKA floating point) numbers? Round-off error! FLOPS: Floating Point Operations Per Second

54
One Last Thing… Real valued (AKA floating point) numbers? Round-off error! FLOPS: Floating Point Operations Per Second

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google