Data Representation

Data Representation Computer Architecture 2nd Semester 2009-2010

Basic Idea DATA

In text of decimal format

Computer System

10010100101010 RAM 101101010010100101001010010100100101001010101

Data Representation 

Computer operation mechanism › Binary Numbers (on / off)

 It

is good to know binary numbers, decimal, hexadecimal numbers & the relationships of these number systems to understand the internal processing of computer

Data Representation Unit & processing unit  Binary

Number in Circuit

› On / Off › High / Low

Binary and Decimal Conversion Decimal Numbers 0 1 2 3 4 5 6 7 8 9 10

Binary Numbers 0 1 10 11 100 101 110 111 1000 1001 1010

BITS A

Binary Digit(BiT) › Is a digit of Binary System represented

by 1or 0 › A smallest unit that represents data inside the computer › 1 bit can represent 2 values = {1,0} › 2 bits can represent 4 values = {00,01,10,11}

Question  To

the minimum of how many bits we need to represent the 26 English Alphabet plus the alphanumeric 0 to 9 a)5 b)6 c)7 d)8

BYTE A

unit that represents with 8 bit 1 character or number › {00000001, 00000010, 00000011 …..

11111111}

› › Question: How many combinations that

a byte can provide a)64 b)128 c)256 d)512

›

Word  If

the computer’s internal operation were performed on the bit basis, the operation speed would be too low.  For that reason, the idea of processing using a unit called word was born

Word  Over

10 yrs ago, PC operated on word consisting of 16 bits.  Currently, mainstream PCs use words each consisting of 32 and 64 bits

Binary System and Hexadecimal  Information

Processing

› Binary System is used to simplify the

structure of electronic circuit that make up a computer › (255)10 vs (11111111)2  binary is hard to understand Solution – use haxadecimal

Binary System and Hexadecimal  Hexadecimal

number

› Numeric value represented by 16

numeral (0-15). When becomes 16, a carry occurs

Base 2,10 & 16 Table 0 0 1 0 1 1 0 1

2

D

Decimal

Binary

Haxadecimal

0

0

0

1

1

1

2

10

2

3

11

3

4

100

4

5

101

5

6

110

6

7

111

7

8

1000

8

9

1001

9

10

1010

A

11

1011

B

12

1100

C

13

1101

D

14

1110

E

15

1111

F

16

10000

10

17

10001

11

18

10010

12

19

10011

13

20

10100

14

Radix and “weight” 

1,234 › 1 thousand 2 hundred 3 tens and 4 units › (1 x 103) + (2 x 102) + (3 x 101) + (4 x 100)

› Radix

Exponent Weight

Question: Using the weight, a decimal number 32,425 would be represented as?

Binary Digits “weight” and its meaning  The

radix of decimal system is 10 and the radix of binary system is 2.  Ex: 1 1 1 1 1 0 0 1 1 1 0 

1

1

1

1

1

0

0

1

1

1

0

210

29

28

27

26

25

24

23

22

21

20

256

128

64

8

4

2

1024 512 Question:

Using the weight, a binary number 11110111 would be represented as?

Auxiliary units & power representation Unit symbol

Remarks

Unit that represent T (tera) large amount G (giga) M (mega) k (kilo)

Exponent notation 1012 109 106 103

Units that represent m (milli) small amonts µ (micro) n (nano) p (pico)

10-3 10-6 10-9 10-12

1 / 1,000 1 / 1,000,000 1 / 1,000,000,000 1 / 1,000,000,000,000

~ 240 ~ 230 ~ 220 ~ 210

Addition of Binary Numbers 0

+ 0 + 1 + 1 +

0 1 0 1

Question: 11010 + 1100

= = = =

0 1 1 10

Subtraction of Binary Numbers 0

0 1 1 -

0 1 0 1

Question: 11010 - 1100

= = = =

0 -1 1 0