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Systems Architecture, Fourth Edition 1 Data Representation Chapter 3.

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Presentation on theme: "Systems Architecture, Fourth Edition 1 Data Representation Chapter 3."— Presentation transcript:

1 Systems Architecture, Fourth Edition 1 Data Representation Chapter 3

2 Systems Architecture, Fourth Edition2 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

3 Systems Architecture, Fourth Edition3 Automated Data Processing Processing is implemented with electrical switches which are combined to form processing circuits. For Example: A + B = C

4 Systems Architecture, Fourth Edition4 Automated Data Processing

5 Systems Architecture, Fourth Edition5 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

6 Systems Architecture, Fourth Edition6 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)

7 Systems Architecture, Fourth Edition7 Binary Data Representation

8 Systems Architecture, Fourth Edition8 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) = (3 x.1) + (6 x.01) + (8 x.001) = 0.3 + 0.06 + 0.008 = 0.368 0.3 + 0.06 + 0.008 = 0.368

9 Systems Architecture, Fourth Edition9 Binary Data Representation

10 Systems Architecture, Fourth Edition10 Binary Data Representation

11 Systems Architecture, Fourth Edition11 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.

12 Systems Architecture, Fourth Edition12 Binary Data Representation

13 Systems Architecture, Fourth Edition13 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)

14 Systems Architecture, Fourth Edition14 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.

15 Systems Architecture, Fourth Edition15 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.

16 Systems Architecture, Fourth Edition16 Goals of Computer Data Representation Standardization - various organizations have created standard data encoding methods for communication among computer systems and their components.

17 Systems Architecture, Fourth Edition17 CPU Data Types Five Primitive Data Types: 1. Integer  Excess Notation  Two’s Complement Notation 2. Real number  Floating Point Notation 3. Character 4. Boolean 5. Memory address

18 Systems Architecture, Fourth Edition18 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

19 Systems Architecture, Fourth Edition19 CPU Data Types

20 Systems Architecture, Fourth Edition20 CPU Data Types Two’s 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

21 Systems Architecture, Fourth Edition21 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

22 Systems Architecture, Fourth Edition22 CPU Data Types Real Number

23 Systems Architecture, Fourth Edition23 CPU Data Types Scientific Notation

24 Systems Architecture, Fourth Edition24 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

25 Systems Architecture, Fourth Edition25 CPU Data Types Floating Point Notation

26 Systems Architecture, Fourth Edition26 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.

27 Systems Architecture, Fourth Edition27 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 - (2 6 ) symbols are represented.

28 Systems Architecture, Fourth Edition28 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 - (2 8 ) symbols are represented.

29 Systems Architecture, Fourth Edition29 CPU Data Types 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 : ; ? 4 @ 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 : ; ? 4 @ 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 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 : ; ? 4 @ 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

30 Systems Architecture, Fourth Edition30

31 Systems Architecture, Fourth Edition31 CPU Data Types

32 Systems Architecture, Fourth Edition32 CPU Data Types Unicode:  Multilingual character encoding standard encompassing all of the world’s written languages.  Characters are coded using 16 bit strings.  65,535 (2 16 ) characters are represented.

33 Systems Architecture, Fourth Edition33 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.

34 Systems Architecture, Fourth Edition34 CPU Data Types Memory Addresses: 1. Flat memory model: Memory addresses can be represented using a single integer. 2. Segmented memory model: Memory addresses require multiple integers. Memory addresses require multiple integers.

35 Systems Architecture, Fourth Edition35 Data Structures

36 Systems Architecture, Fourth Edition36 Data Structures

37 Systems Architecture, Fourth Edition37 Data Structures

38 Systems Architecture, Fourth Edition38 Data Structures

39 Systems Architecture, Fourth Edition39 Data Structures

40 Systems Architecture, Fourth Edition40 Data Structures

41 Systems Architecture, Fourth Edition41 Data Structures

42 Systems Architecture, Fourth Edition42 Data Structures

43 Systems Architecture, Fourth Edition43 Data Structures

44 Systems Architecture, Fourth Edition44 Data Structures

45 Systems Architecture, Fourth Edition45 Data Structures

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