1. 1 Computer Fundamental ITD1382 Coursework : 100% 1. Tests 2. Quizzes (Short) 3. Assignments Module Value : 3.0

2. 2 Course Content Numbering System (Binary, Hexadecimal …) Logic Systems and Digital Circuits Computer Systems Architecture Hardware Components System Resources The Boot Process Assembling a Computer Hardware and OS Maintenance Operating System Fundamentals Windows Operating Systems (Windows 2003 Server / XP Professional) Linux Operating Systems (Red Hat / Fedora Core)

3. 3 Teaching Materials Lecture Notes Tutorial Exercises / Solutions Tests & Quizzes / Solutions Lab Sheets Textbook - Cisco Networking Academy Program IT Essential I: PC Hardware and Software Companion Guide, Cisco Press 2004. Reference book – Cisco Networking Academy Program IT Essential II: Network Operating System Companion Guide, Cisco Press 2003. Note: Download from webct ( http://webct.vtc.edu.hk )

4. 4 Lecture 1 Numbering System

5. 5 Numbering Systems in Computer Binary (Base 2) e.g. 101111 2 Octal (Base 8) e.g. 16 8 (Digit with value 0 -7) Hexadecimal (or Hex - Base 16) ABCDEF 16 (Digit with value 0 – F) How to convert between different base?

6. 6 Conversion from decimal to binary Example: Convert 345 (in decimal) to binary 345 MOD 2= 1(345/2 = 172) 172 MOD 2= 0(172/2 = 86) 86 MOD 2= 0(86/2 = 43 ) 43 MOD 2= 1(43/2 = 21 ) 21 MOD 2= 1(21/2 = 10 ) 10 MOD 2= 0(10/2 = 5 ) 5 MOD 2= 1(5/2 = 2 ) 2 MOD 2= 0(2/2 = 1 ) 1 MOD 2= 1(1/2 = 0 ) Ans: 1 0101 1001

7. 7 Conversion from Binary, Octal, Hexadecimal to Decimal - Power Series Example convert 1 0101 1001 to decimal Decimal representation of 1 0101 1001 = 1x2 8 + 0x 2 7 + 1x 2 6 + 0x2 5 + 1x2 4 + 1x2 3 + 0x2 2 + 0x2 1 +1X2 0 = 345 10 Example Convert 531 8 (oct) to decimal Decimal representation of 531 8 =5x8 2 + 3x8 1 + 1x8 0 = 345 10

8. 8 Conversion from Binary to Octal Conversion from binary to oct 101 011 001 531=> 531 (oct) By using MOD 8 and (MOD – find the remainder) Binary to Octal 0000 0011 0102 0113 1004 1015 1106 1117

9. 9 Conversion from Binary to Hexadecimal Conversion from binary to hex 101011001 159=> 159 (hex) By using MOD 16 (MOD – find the remainder) Binary to Hexidecimal 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019 1010A 1011B 1100C 1101D 1110E 1111F

10. 10 Conversion from decimal to octal or hexadecimal Example Convert 345 10 to octal representation 345 MOD 8= 1(345/8 = 43) 43MOD 8= 3(43/8 = 5 ) 5MOD 8= 5 Ans: 531 8 Example Convert 345 10 to hexadecimal representation 345MOD 16= 9(345/16 = 21) 21MOD 16= 5(21/16 = 1 ) 1MOD 16= 1 Ans: 159 16

11. Conversion from decimal to binary Example Convert 0.8125 10 to binary representation 0.8125x 2= 1 + 0.625 0.625x 2= 1+ 0.25 0.25x 2= 0+0.5 0.5x 2= 1+0.0 Ans: 0.1101 2 Convert to decimal rep.: Stop or: 1x2 -1 +1x2 -2 +0x2 -3 +1x2 -4

12. 12 Conversion from decimal to octal Example Convert 0.8125 10 to octal representation 0.8125x 8= 6+ 0.5 0.5x 8= 4+ 0.0 Ans: 0.64 8 Stop

13. 13 Arithmetic Operation (Binary) Addition BinaryDecimal Carries00011 Augend1001119 Addend0101111 Sum01111030 Augend+ Addend= Sum 19+11= 30 10011+01011= 11110

14. 14 Arithmetic Operation (Binary) Subtraction e.g. BinaryDecimal Borrows11000 Minuend11011054 Subtrahend01101026 Difference01110028 If Subtrahend > Minuend? => NEGATIVE NUMBER

15. 15 Arithmetic Operation (Binary) e.g. BinaryDecimal Borrows110000 Minuend 10011038 Subtrahend 11001050 Difference?110100?? Negative number ? How negative number is represented in binary format?

16. 16 Signed Number How to represent negative number (binary number) Use a sign bit i.e. 0 represent positive and 1 represent negative e.g. +10 => 0 1010 and -10 => 1 1010 Problem with two zero i.e. 00000 or 10000 So, it may not be a good solution for representing binary number.