CS170 Computer Organization and Architecture I

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

2. Outline • What is a computer? • An overview of number systems • Decimal • Binary • Octal • Hexadecimal CS170 Fall 2002

3. 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

4. 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

5. 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, .., 9 binary (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 0 i positional notation 3 7 5 d 5 * 100 = 5 7 * 101 = 70 3 * 102 = 300 Three hundred and seventy five CS170 Fall 2002

6. Conversion from binary to decimal Convert 10112 to decimal 3 2 1 0 i 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

7. Conversion from decimal 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 Convert 1310 to binary Operation Quotient remainder 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

8. Conversion from decimal to binary Previous approach can be used to convert from decimal to any number system Convert 1310 to octal (octal is base 8) Operation Quotient remainder 13 by 8 1 5 1 by 8 0 1 1310 = 158 158= (5 * 80) + (1 * 81) = 1310 CS170 Fall 2002

9. 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) CS170 Fall 2002

10. 1101001110 11 0100 1110 416 Conversion from binary to hex Convert 11010011102 to hex Divide binary number into 4 bits groups from right to left 316 E16 34E16 CS170 Fall 2002

11. Decimal Binary Hexadecimal 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 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 20 = 1 27 = 128 21 = 2 28 = 256 22 = 4 29 = 512 23 = 8 210 = 1024 24 = 16 211 = 2048 25 = 32 212 = 4096 26 = 64 213 = 8190 Kilo 210 Tera 240 Mega 220 Peta 250 Giga 230 CS170 Fall 2002