1. Lecture 1: 8/27/2002CS170 Fall 20021 CS170 Computer Organization and Architecture I Ayman Abdel-Hamid Department of Computer Science Old Dominion University Lecture 1: 8/27/2002

2. CS170 Fall 20022 Outline What is a computer? An overview of number systems Decimal Binary Octal Hexadecimal

3. Lecture 1: 8/27/2002CS170 Fall 20023 Processor Memory A Computer Input Output Five classic components of a computer: Input, Output, Memory, Data path, Control TapesKeyboardMousescanner DisplayPaper Processor

4. Lecture 1: 8/27/2002CS170 Fall 20024 Computers are built on two key principles 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 Both instructions and data are represented by numbers Instructions and data are stored in memory and are read and written as numbers

5. Lecture 1: 8/27/2002CS170 Fall 20025 Number Systems 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 “number B ” (375 in decimal is written 375 10, 1011 in binary is written 1011 2 ) Value of i th digit d is “d * B i” where i starts from 0 and increases from right to left 2 1 0ipositional notation 3 7 5d 5 * 10 0 =5 7 * 10 1 =70 3 * 10 2 =300 Three hundred and seventy five

6. Lecture 1: 8/27/2002CS170 Fall 20026 Conversion from binary to decimal Convert 1011 2 to decimal = (1 * 2 0 ) + (1 * 2 1 ) + (0 * 2 2 ) + (1 *2 3 ) = 1 + 2 + 0 + 8 = 11 10 3 2 1 0i 1 0 1 1 d This process can be used for conversion from any number system to decimal (TRY convert 123 8 to decimal)

7. Lecture 1: 8/27/2002CS170 Fall 20027 Conversion from decimal to binary Convert 13 10 to binary 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 OperationQuotientremainder 13 by 2 6 1 6 by 2 3 0 3 by 2 1 1 1 by 2 0 1 13 10 = 1101 2

8. Lecture 1: 8/27/2002CS170 Fall 20028 Conversion from decimal to binary Convert 13 10 to octal (octal is base 8) Previous approach can be used to convert from decimal to any number system OperationQuotientremainder 13 by 8 1 5 1 by 8 0 1 13 10 = 15 8 15 8 = (5 * 8 0 ) + (1 * 8 1 ) = 13 10

9. Lecture 1: 8/27/2002CS170 Fall 20029 Other Number Systems 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)

10. Lecture 1: 8/27/2002CS170 Fall 200210 Conversion from binary to hex Convert 1101001110 2 to hex Divide binary number into 4 bits groups from right to left 1101001110 3 16 4 16 E 16 34E 16 1101001110

11. Lecture 1: 8/27/2002CS170 Fall 200211 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 2 0 = 12 7 = 128 2 1 = 22 8 = 256 2 2 = 42 9 = 512 2 3 = 82 10 = 1024 2 4 = 162 11 = 2048 2 5 = 322 12 = 4096 2 6 = 642 13 = 8190 Kilo 2 10 Tera2 40 Mega 2 20 Peta2 50 Giga2 30