Computer Architecture & Operating Systems: University Of Colombo School Of Computing

UNIVERSITY OF COLOMBO SCHOOL OF COMPUTING

IT2101 Computer Architecture & Operating Systems DEGREE OF BACHELOR OF INFORMATION TECHNOLOGY

Major Topics 1. Review of Basic Principles 07 2. General Systems Architecture 04 3. Instruction Set Architecture 05 4. Basic CPU Architecture 04 5. Memory Hierarchy & I/O Techniques 06 6. Parallelism 04 7. Introduction to Operating Systems 04 8 Processes & Process Management 08 9. Memory Management Total Lectures 60 06 10. File Systems

Review of Basic Principles (7hrs.) • Radix number systems • Decimal, Binary, and Hexadecimal number systems • Binary arithmetic: addition, complements, and subtraction • Binary Codes • BCD code • ASCII character code • Boolean algebra and Logic Gates: • Boolean functions • Logic Gates: AND, OR, NOT, NOR, NAND, XOR • Simplification of Boolean functions:(2,3, and 4 variable Karnaugh maps)

Review of Basic Principles • Digital Computer – A digital system performing computational tasks. – Represents information using variables that take a limited number of discrete values. – Processes these values internally – Uses two basic values to represent information

Radix Number Systems Each number system has a number of different digits which is called the radix or the base of the number system. • Decimal Base = 10 • Binary Base = 2 • Octal Base = 8 • Hexadecimal (Hex) Base = 16

Decimal Number System

Base (Radix) Digits e.g.

10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 747510

The magnitude represented by a digit is decided by the position of the digit within the number. 1000 100

7

4

10

1

7

5

For example the digit 7 in the left-most position of 7475 counts for 7000 and the digit 7 in the second position from the right counts for 70.

Binary Number System Base (Radix) Digits e.g.

2 0, 1 11102

8=23 4=22 2=21 1=20

1

1

1

0

The digit 1 in the third position from the right represents the value 4 and the digit 1 in the fourth position from the right represents the value 8.

Octal Number System Base (Radix) Digits e.g.

8 0, 1, 2, 3, 4, 5, 6, 7 16238

512=83 64=82

1

6

8=81

2

1=80

3

The digit 2 in the second position from the right represents the value 16 and the digit 1 in the fourth position from the right represents the value 512.

Hexadecimal Number Base (Radix) 16 System Digits

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F 2F4D 16

e.g.

4096=16 256=16

16=16

3

1

2

2

F

4

1=160

D

The digit F in the third position from the right represents the value 3840 and the digit D in the first position from the right represents the value 1.

Binary Arithmetic • Addition

•Complements •Subtraction

Binary Addition (a)

(c)

0 +0 0 1 +0 1

0 +1 1

(b)

(d)

1 +1 10

Carry Bit

Binary Addition Examples 1011 + 1100 10111

(a)

(d)

101 + 1001 1110

(b)

1010 + 100 1110

(c)

1011 + 101 10000

10011001 + 101100 11000101

(e)

Binary Complement (1s Complement) Operation

1

0

0

1

Example

110010110 001101001

Two’s Complement The Two’s complement of a binary number is obtained by first complementing the number and then adding 1 to the result. 1001110

0110001 + 1

One’s Complement

0110010

Two’s Complement

Binary Subtraction Binary subtraction is implemented by adding the Two’s complement of the number to be subtracted. Two’s Example

1101 -1001

compleme nt of 1001

1101 +0111 10100

If there is a carry then it is ignored. Thus, the answer is 0100.

Binary Codes A binary code is a group of n bits that assume up to 2n distinct combinations of 1’s and 0’s with each combination representing one element of the set that is being coded. • BCD – Binary Coded Decimal • ASCII – American Standard Code for Information Interchange

BCD – Binary Coded Decimal Decimal When the decimal numbers are represented in BCD, each decimal digit is represented by the equivalent BCD code. Example :BCD Representation of Decimal 6349 6

3

4

0110 0011 0100

9

Number

BCD Number

0 1 2 3 4 5 6 7 8 9

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001

ASCII Number ASCII 0 1 2 3 4 5 6 7 8 9

0110000 0110001 0110010 0110011 0110100 0110101 0110110 0110111 0111000 0111001

Letter A B C D E F G H I

ASCII 1000001 1000010 1000011 1000100 1000101 1000110 1000111 1001000 1001001

ASCII

Continued.

Letter ASCII J 1001010 K 1001011 L 1001100 M 1001101 N 1001110 O 1001111 P 1010000 Q 1010001 R 1010010

Letter ASCII S 1010011 T 1010100 U 1010101 V 1010110 W 1010111 X 1011000 Y 1011001 Z 1011010

Logic Gates • Binary information is represented in digital computers by physical quantities called signals. • Two different electrical voltage levels such as 3 volts and 0.5 volts may be used to represent binary 1 and 0. • Binary logic deals with binary variables and with operations that assume a logical meaning.

Logic Gates

Contd…

• A particular logic operation can be described in an algebraic or tabular form. • The manipulation of binary information is done by the circuits called logic gates which are blocks of hardware that produce signals of binary 1 or 0 when input logic requirements are satisfied.

Logic Gates

Contd…

• Each gate has a distinct graphics symbol and it’s operation can be described by means of an algebraic expression or in a form of a table called the truth table. • Each gate has one or more binary inputs and one binary output.

Logic Gates AND OR NOT (Inverter) NAND (Not AND) NOR (Not OR) XOR (Exclusive-OR) Exclusive-NOR

Logic Gates

Cont.

AND Logic Gate Table

Truth

AB x 0 0 0 1 1 0 x=A.B A, B Binary Input Variables 1 1 x Binary Output Variable A B

x 0 0 0 1

Logic Gates

Cont.

Logic Gate Table

OR A B

x=A+B This is read as x equals A or B.

Truth x

A 0 0 1 1

B 0 1 0 1

x 0 1 1 1

Logic Gates

Cont.

NOT Logic Gate Table A

x= A

Truth x

A x 0 1 1 0

Logic Gates NAND

Cont.

Logic Gate

A B

x=A.B

Truth Table x

AB 0 0 0 1 1 0 1 1

x 1 1 1 0

Logic Gates

Cont.

NORLogic Gate Table A B

x=A+B

x

Truth A 0 0 1 1

B 0 1 0 1

x 1 0 0 0

Logic Gates

Cont.

XORLogic Gate Table A B

x=A+B

x

Truth A 0 0 1 1

B 0 1 0 1

x 0 1 1 0

Logic Gates

Cont.

Exclusive-NOR Logic Gate A B

x=A+B

x

Truth Table A 0 0 1 1

B 0 1 0 1

x 1 0 0 1

Contact External Degree Unit (EDU) of the University of Colombo School of Computing No. 221/2A, Dharmapala Mawatha, Colombo 7. Phone : 074-720511 Fax : 074-720512

http://www.bit. lk

Thank you