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Data Representation

- Chapter 3

Data Representation and Processing

- Data and information processors must be able to
- Recognize external data and convert it to an

appropriate internal format - Store and retrieve data internally
- Transport data among internal storage and

processing components - Manipulating data to produce results or decisions

Automated Data Processing

- Processing is implemented with electrical

switches which are combined to form processing

circuits. - For Example A B C

Automated Data Processing

Binary Data Representation

- Computers use binary numbers
- Binary numbers correspond directly with values in

boolean logic. - Computers combine multiple digits to form a

single data value to represent large numbers.

http//math.hws.edu/TMCM/java/DataReps/

http//nickciske.com/tools/binary.php

Binary Data Representation

- Numbering System Characteristics
- The number of characters in the number system is

equal to the base of the number system. - There are 10 characters in the decimal number

system. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) - There are 2 characters in the binary number

system. (0, 1)

Binary Data Representation

Binary Data Representation

- The fractional part of a numeric value is

separated from the whole number by a period

(radix point) - For Example 5,689.368
- (3 x .1) (6 x .01) (8 x .001)
- 0.3 0.06 0.008 0.368

Binary Data Representation

Binary Data Representation

Binary Data Representation

- Hexadecimal Notation
- The base (radix) of a hexadecimal number system

is 16. - There are 16 characters in the hexadecimal number

system. - There are only 10 characters in the Arabic number

system that can be used to represent some of the

16 characters in the hexadecimal number system. - The letters A, B, C, D, E, F are used to

represent the last 6 characters in the

hexadecimal number system.

Binary Data Representation

Binary Data Representation

- Octal Notation
- Some operating systems and machine language

programs use octal notation. - The base (radix) of an Octal number system is 8.
- There are 8 characters in the octal number

system. (0, 1, 2, 3, 4, 5, 6, 7)

Goals of Computer Data Representation

- Compactness - compact data representation

requires less storage space and less expensive

processing and storage devices. - Accuracy - the accuracy of representation

increases with the number of data bits used.

Goals of Computer Data Representation

- Range routine calculations can generate

quantities that are either too large or too small

to be stored within finite circuitry. - Ease of manipulation - the efficiency of a

processor depends on its complexity.

Goals of Computer Data Representation

- Standardization - various organizations have

created standard data encoding methods for

communication among computer systems and their

components.

CPU Data Types

- Five Primitive Data Types
- Integer
- Excess Notation
- Twos Complement Notation
- Real number
- Floating Point Notation
- Character
- Boolean
- Memory address

CPU Data Types

- Integer
- An integer is a whole number (For example 3, 5,

6) - Integers can be signed or unsigned
- A signed integer uses one bit to represent the

sign - The sign bit is the high order bit
- Excess notation is used to represent signed

integers

CPU Data Types

CPU Data Types

- Twos Complement Notation
- Nonnegative integer values are represented as

ordinary binary numbers - Negative integer values are represented using

(Complement of positive value 1) - The complement of a number is formed by changing

all 1 bits to 0 and all 0 bits to 1

CPU Data Types

- Real Numbers
- A real number can contain both whole and

fractional components - The whole portion appears to the left of the

radix point - The fractional portion appears to the right of

the radix point

CPU Data Types

Real Number

CPU Data Types

Scientific Notation

CPU Data Types

- Floating Point Notation
- Floating point notation is used to represent very

small numbers and very large numbers - Values can either be very large or very small,

but not both at the same time

CPU Data Types

Floating Point Notation

CPU Data Types

- Character Data
- An individual symbol is a character.
- Characters grouped together form a string.
- Character data can only be represented in the

computer system using a coding scheme.

CPU Data Types

- Binary Coded Decimal (BCD)
- Character coding method used by early IBM

mainframe computers. - Characters are encoded as strings of six bits.
- 64 - (26) symbols are represented.

CPU Data Types

- Extended Binary Coded Decimal Interchange Code
- 8 bit coding method used by IBM mainframe

computers. - Characters are encoded as strings of eight bits.
- 256 - (28) symbols are represented.

CPU Data Types

0 1 2 3 4 5 6 7 8 9 A B

C D E F 0 NUL SOH STX ETX EOT ENQ ACK BEL

BS HT LF VT FF C SO SI 1 DLE DC1 DC2 DC3

DC4 NAK SYN ETB CAN EM SUB ESC FS GS RS US 2

SP ! " ' ( )

, - . / 3 0 1 2 3 4 5 6 7

8 9 lt gt ? 4 _at_ A B C

D E F G H I J K L M N O 5

P Q R S T U V W X Y Z \

_ 6 a b c d e f g h

i j k l m n o 7 p q r s t

u v w x y z DEL

- American Standard Code of Information

Interchange - Coding method used in data communication that has

been adopted by the United States. - 7-bit and 8-bit formats
- Includes device control codes

0 1 2 3 4 5 6 7 8 9 A B

C D E F 0 NUL SOH STX ETX EOT ENQ ACK BEL

BS HT LF VT FF C SO SI 1 DLE DC1 DC2 DC3

DC4 NAK SYN ETB CAN EM SUB ESC FS GS RS US 2

SP ! " ' ( )

, - . / 3 0 1 2 3 4 5 6 7

8 9 lt gt ? 4 _at_ A B C

D E F G H I J K L M N O 5

P Q R S T U V W X Y Z \

_ 6 a b c d e f g h

i j k l m n o 7 p q r s t

u v w x y z DEL

0 1 2 3 4 5 6 7 8 9 A B

C D E F 0 NUL SOH STX ETX EOT ENQ ACK BEL

BS HT LF VT FF CR SO SI 1 DLE DC1 DC2 DC3

DC4 NAK SYN ETB CAN EM SUB ESC FS GS RS US 2

SP ! " ' ( )

, - . / 3 0 1 2 3 4 5 6 7

8 9 lt gt ? 4 _at_ A B C

D E F G H I J K L M N O 5

P Q R S T U V W X Y Z \

_ 6 a b c d e f g h

i j k l m n o 7 p q r s t

u v w x y z DEL

(No Transcript)

CPU Data Types

CPU Data Types

- Unicode
- Multilingual character encoding standard

encompassing all of the worlds written

languages. - Characters are coded using 16 bit strings.
- 65,535 (216) characters are represented.

CPU Data Types

- Boolean Data
- Two data values true and false.
- Data is represented using a single bit.
- Binary 1 can represent true and binary 0 can

represent false.

CPU Data Types

- Memory Addresses
- Flat memory model Memory addresses can be

represented using a single integer. - Segmented memory model
- Memory addresses require multiple integers.

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures

Data Structures