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CS170 Computer Organization and Architecture I

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CS170 Computer Organization and Architecture I

Ayman Abdel-Hamid

Department of Computer Science

Old Dominion University

Lecture 1: 8/27/2002

CS170 Fall 2002

- What is a computer?
- An overview of number systems
- Decimal
- Binary
- Octal
- Hexadecimal

CS170 Fall 2002

Input

Output

A Computer

Processor

Tapes

Keyboard

Mouse

scanner

Display

Paper

Memory

Five classic components of a computer:

Input, Output, Memory, Data path, Control

Processor

CS170 Fall 2002

Computers are built on two key principles

- Both instructions and data are represented by numbers
- Instructions and data are stored in memory and are read and written as numbers

All computers use the binary number system (base 2)

(basic nature of electronic circuits ON/OFF, current flow/does not flow)

Machine alphabet has two letters “0”, “1”

Each letter is a binary digit “bit”. Byte is 8 bits

CS170 Fall 2002

- Numbers can be represented in any base (humans use base 10)
- Symbols for a number system of base B are 0, 1, 2, …, B –1
- decimal (base 10) 0, 1, 2, .., 9binary (base 2) 0, 1
- notation “numberB” (375 in decimal is written 37510, 1011 in binary is written 10112)
- Value of ith digit d is “d * Bi” where i starts from 0 and increases from right to left

2 1 0ipositional notation

3 7 5d

5 * 100=5

7 * 101=70

3 * 102=300

Three hundred and seventy five

CS170 Fall 2002

Convert 10112 to decimal

3 2 1 0i

1 0 1 1 d

= (1 * 20) + (1 * 21) + (0 * 22) + (1 *23)

= 1 + 2 + 0 + 8

= 1110

This process can be used for conversion from any number system to decimal (TRY convert 1238 to decimal)

CS170 Fall 2002

Step 1: divide value by 2 and record remainder

Step 2: as long as quotient not zero, continue to divide the newest quotient by 2 and record the remainder

Step 3: when obtain a zero as quotient, binary representation consists of remainders listed from right to left in order

Convert 1310 to binary

OperationQuotientremainder

13 by 2 6 1

6 by 2 3 0

3 by 2 1 1

1 by 2 0 1

1310 = 11012

CS170 Fall 2002

Previous approach can be used to convert from decimal to any number system

Convert 1310 to octal (octal is base 8)

OperationQuotientremainder

13 by 8 1 5

1 by 8 0 1

1310 = 158

158= (5 * 80) + (1 * 81) = 1310

CS170 Fall 2002

- Octal (base 8)
- Symbols (0, 1, 2, 3, 4, 5, 6, 7)

- Working with too long binary numbers is a problem
- Hexadecimal (base 16)
- Symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)

- Byte = 8 bits = 2 hex digits ( 1 hex digit is 4 bits)

CS170 Fall 2002

1101001110

11

0100

1110

416

Convert 11010011102 to hex

Divide binary number into 4 bits groups from right to left

316

E16

34E16

CS170 Fall 2002

DecimalBinaryHexadecimal

00000 0

10001 1

20010 2

30011 3

40100 4

50101 5

60110 6

70111 7

81000 8

91001 9

101010 A

111011 B

121100 C

131101 D

141110 E

151111 F

20 = 127 = 128

21 = 228 = 256

22 = 429 = 512

23 = 8210 = 1024

24 = 16211 = 2048

25 = 32212 = 4096

26 = 64213 = 8190

Kilo 210Tera240

Mega 220Peta250

Giga230

CS170 Fall 2002