Course : AIT 204

Course Title : Computer Organization and Architecture (COA)

Course Credits : 3 + 0

Course Teacher : Dr. Y R Ghodasara & Prof. K. C. Kamani

College of Agricultural Information Technology

Anand Agricultural University

Anand

Unit I

Explain Booting Process of a Computer

Step 1 : Power On

Step 2 : SMPS(Switch Mode Power Supply) will convert AC current to DC current and

split current to different voltage levels. This will give current to all components

of the motherboard.

Step 3 : BIOS Chip(Basic Input Output System) gets the control and POST

(Pre Operation Self Test) routines are executed to check your hardware.

Step 4 : If POST routines are executed successfully, BIOS will read first sector of the

hard disk. This sector is called MBR(Master Boot Record) sector.(512 bytes)

Step 5 : The instructions in MBR sector are executed and operating system is loaded

in memory.

Step 6 : Computer is booted.

DigitalThe word digital implies that the information is represented by variables that take limited number of discrete states.

Definitions

AnalogThe word analog implies that the information is represented by variables that take many discrete states.

HardwareThe hardware of computer consist of all the electronic components and electro mechanical devices present in the computer.Example : CD Drive, Hard disk, RAM, Processor

SoftwareThe computer software consist of instructions and data that the computer manipulates to perform data processing. Example : Operating systems, compilers, Word, Excel, Power point

FirmwareIn an electronic component, software is permanently written in hardware. This type of electronic component is called firmware.Example : BIOS Chip, Washing Machine Chip, Set top Box Chip

ProgramA sequence of instructions for the computer is known as program.

Computer ArchitectureComputer architecture deals with the structure and behaviour of various functional mode use of the computer.

Computer OrganizationComputer organization deals with the way hardware components are connect together to form a computer system.

Computer DesignComputer design deals with the development of hardware for the computer according to the given set of specifications.

Block Diagram of a Digital Computer

The hardware of a computer is divided into three major parts.

1. CPU (Central Processing Unit)2. RAM (Random Access Memory)3. IOP (Input Output Processor)

RAM

CPU

IOP Output DeviceInput Device

CPUThe central processing unit contains an arithmetic and logical unit which manipulates data, number of registers to store data and control circuits for fetching and executing instructions.

RAMThe memory of a computer contains storage for instructions and data. It is called random access memory because the processor can access any location in memory at random and retrieve binary information with in a fixed interval of time.

IOPThe input output processor contains electronic circuits for communicating and controlling the transfer of information between the computer and outside world. The input output devices connected to the computer are keyboard, mouse, printer, monitor, disk drive etc.

Number SystemsFollowing number systems are used in the computer.

Binary SystemBinary system contains two symbols. 0,1

Octal SystemOctal system contains eight symbols.0,1,2,3,4,5,6,7

Decimal SystemDecimal system contains ten symbols.0,1,2,3,4,5,6,7,8,9

Hexa Decimal SystemHexa decimal system contains sixteen symbols.0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

Number System Conversion

Binary Octal Decimal Hexa Decimal

0000 1111

77

100

AF

0000 0011 1111 1010

1270

512

10F

Representation of Information

Alpha Numeric InformationThe alpha numeric information like name of the student, college name etc. represented by string of characters. This information is represented by ASCII or EASCII or UNICODE character set format.

ASCIIThe full form of ASCII is American Standard Code for Information Interchange.ASCII is a seven bit binary representation.It can represent 128 different symbols.

EASCIIThe full form of EASCII is Extended American Standard Code for Information Interchange.EASCII is a eight bit binary representation.It can represent 256 different symbols.

UNICODEThe ASCII and EASCII character set can represent only upper and lower case alphabet.Other languages characters are necessary to develop multilingual systems.Unicode character set represents character from different languages like Japanese, Korean, South Asian languages.Unicode character set is a 16-bit representation of the symbol.

Unsigned Integer RepresentationUnsigned Integer Numbers are the numbers with positive sign. Unsigned Integer Numbers are represented using unsigned integer representation scheme.

Examples :

Unsigned Integer 16-bit Representation

0 0000 0000 0000 00001 0000 0000 0000 000164 0000 0000 0100 0000513 0000 0010 0000 00011024 ?1023 ?511 ?

Signed Integer RepresentationSigned Integer Numbers are the numbers with positive and negative sign. Signed Integer Numbers are represented using 2’s complement representation scheme.

Examples :

1. How integer 10 is represented in 16-bit 2’s complement scheme ?

Step 1 : Make binary of 10 0000 0000 0000 1010

2. How integer -10 is represented in 16-bit 2’s complement scheme ?

Step 1 : Make binary of 10 0000 0000 0000 1010

Step 2 : Make Complement 1111 1111 1111 0101Step 3 : Add binary 1 + 1

--------------------------------Step 4 : Make Sum 1111 1111 1111 0110

3. How integer -1 is represented in 16-bit 2’s complement scheme ?4. How integer -512 is represented in 16-bit 2’s complement scheme ?

Floating Point RepresentationThe IEEE 754 standard is use to represent real numbers on the majority of computer systems.

It uses 32-bit pattern to represent single precision numbers and 64-bit pattern to represent double precision numbers.

Single Precision (32-bit) Representation

Double Precision (64-bit) Representation

Equation 1 : ± 1.F X 2E-127 32-bit representationEquation 2 : ± 1.F X 2E-1023 64-bit representation

In both cases, F is preceded with an implied one numeric and of binary point.

If sign bit value is 0 then number is positive and if value is 1 then number is negative.

Sign bit1 – bit

Exponent E8-bit

Fraction F23-bit

Sign bit1 – bit

Exponent E11-bit

Fraction F52-bit

Example 1 : Store 5.5 in 32-bit format

Step 1 : 5.5Step 2 : Make binary representation

101.1Step 3 : Normalize binary representation

1.011 X 22 (± 1.F X 2E-127)Step 4 : Get Exponent

E-127=2E=129

Step 5 : Convert exponent in 8-bit binary1000 0001

Step 6 : Number is positive, sign bit is zero.Step 7 : Convert fractional part in 23-bit binary.

0110 0000 0000 0000 0000 000Step 8 : Put sign bit, exponent and fractional part.

0 1000 0001 0110 0000 0000 0000 0000 000

Example 2 : Convert 0100 0000 1011 0000 0000 0000 0000 0000

Step 1 : 0100 0000 1011 0000 0000 0000 0000 0000Step 2 : Place sign bit, exponent and fractional part

100 0000 1

sign exponent fractional part

Step 3 : Sign bit is zero, number is positive.Step 4 : E=1000 0001 E=129Step 5 : Put values in formula. ± 1. 011 0000 0000 0000 0000 0000 X 2(129-127)

Step 6 : Number is positive, sign bit is zero.Step 7 : Simplify and discard extra zero.

= ± 1.011 X 22

= 101.1= 5.5

0 1000 0001 011 0000 0000 0000 0000 0000

Example 3 : Store 15.5 in 64-bit format

Step 1 : 15.5Step 2 : Make binary representation

1111.1Step 3 : Normalize binary representation

1.1111 X 23 (± 1.F X 2E-1023)Step 4 : Get Exponent

E-1023=3E=1026

Step 5 : Convert exponent in 11-bit binary100 0000 0010

Step 6 : Number is positive, sign bit is zero.Step 7 : Convert fractional part in 52-bit binary.

1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000Step 8 : Put sign bit, exponent and fractional part.

0 100 0000 0010 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

Example 4 : Store -11.75 in 32-bit format

Do it yourself.

Logic GatesLogic gate is a digital circuit created using transistors.Using logic gate more complex digital circuits like register, memory, processor etc. are created.

1. NOT Gate This gate is also known as inverter. It changes logic 1 input to logic 0 or changes logic 0 to logic 1.

A X

Logic NOT

A X

1 0

0 1

Truth Table

X = A’

OR

X = Ā

Boolean Function

2. AND Gate The operation of the AND gate is such that its output is logic 1 only if all of its inputs are logic 1 otherwise the output is logic 0.

A B X

0 0 0

0 1 0

1 0 0

1 1 1

Truth Table

X = AB

OR

X = A.B

Boolean Function

AX

Logic AND

B

3. OR Gate The operation of the OR gate is such that its output is logic 1 if any one input is logic 1 otherwise the output is logic 0.

A B X

0 0 0

0 1 1

1 0 1

1 1 1

Truth Table

X = A+B

Boolean Function

A

X

Logic OR

B

4. Exclusive OR Gate(XOR Gate) The exclusive OR gate is sometimes called parity checker. The exclusive OR gate counts the number of 1s at its input and give output logic 1 for an odd count and logic 0 for even count.

A B X

0 0 0

0 1 1

1 0 1

1 1 0

Truth Table

X = A + B

Boolean Function

A

X

Exclusive OR Gate

B

5. NAND Gate The operation of the NAND gate is complement of AND gate.

A B X

0 0 1

0 1 1

1 0 1

1 1 0

Truth Table

X = (AB)’

OR

X = A.B

Boolean Function

AX

Logic NAND Gate

B

6. NOR Gate The operation of the NOR gate function is complement of OR gate.

A B X

0 0 1

0 1 0

1 0 0

1 1 0

Truth Table

X = (A+B)’

OR

X = A + B

Boolean Function

A

X

Logic NOR Gate

B

7. Exclusive NOR Gate(NOR Gate) The exclusive NOR gate is complement of exclusive OR gate.

A B X

0 0 1

0 1 0

1 0 0

1 1 1

Truth Table

X = A + B

Boolean Function

A

X

Exclusive NOR Gate

B

DefinitionsBoolean Algebra Boolean algebra is an algebra that deals with binary variables and logic operations.Boolean Function Boolean function can be expressed algebraically with binary variables, logic operation symbols, parenthesis and equal sign. For a given values of variables, boolean function can be either 1 or 0. Example : F = X + Y’Z

Truth Table Truth table is a tabular representation of boolean function with different variable values.

Y Y’Z

Z

Y’

X

F

X Y Z Y’ Y’Z F=X+Y’Z

0 0 0 1 0 0

0 0 1 1 1 1

0 1 0 0 0 0

0 1 1 0 0 0

1 0 0 1 0 1

1 0 1 1 1 1

1 1 0 0 0 1

1 1 1 0 0 1

Draw digital circuit using following boolean function.F= A + B’C’

B B’C’

C

A

C’

B’

F = A + B’C’

INPUT OUTPUT

A B C B’ C’ B’C’ F=A+B’C’

0 0 0 1 1 1 1

0 0 1 1 0 0 0

0 1 0 0 1 0 0

0 1 1 0 0 0 0

1 0 0 1 1 1 1

1 0 1 1 0 0 1

1 1 0 0 1 0 1

1 1 1 0 0 0 1

Draw digital circuit using following boolean function.

F= AB + A’CABA

F = AB + A’C

INPUT OUTPUT

A B C AB A’ A’C F=AB+A’C

0 0 0 0 1 0 0

0 0 1 0 1 1 1

0 1 0 0 1 0 0

0 1 1 0 1 1 1

1 0 0 0 0 0 0

1 0 1 0 0 0 0

1 1 0 1 0 0 1

1 1 1 1 0 0 1

B

C

A’A’C

Rules for Boolean Algebra

1. A + 0 = A2. A . 0 = 03. A + 1 = 14. A . 1 = A5. A + A = A6. A . A = A7. A + A’ = 18. A + B = B + A9. A . A’ = 010. AB = BA11. A + (B + C) = (A + B) + C12. A.(BC) = (AB).C13. A . (B+C) = AB + AC14. A + BC =(A+B).(A+C)15. (A+B)’ = A’B’16. (AB)’ = A’ + B’17. (A’)’ = A

Circuit Simplification Using Boolean Algebra RulesExample 1 Boolean Function F=ABC + ABC’ + A’C

ABCA

F = ABC + ABC’ + A’C

BC

ABC’

A’C

INPUT OUTPUT

A B C ABC C’ ABC’ A’ A’C F=ABC+ABC’+A’C

0 0 0 0 1 0 1 0 0

0 0 1 0 0 0 1 1 1

0 1 0 0 1 0 1 0 0

0 1 1 0 0 0 1 1 1

1 0 0 0 1 0 0 0 0

1 0 1 0 0 0 0 0 0

1 1 0 0 1 1 0 0 1

1 1 1 1 0 0 0 0 1

Circuit SimplificationF = ABC + ABC’ + A’C = AB [ C + C’ ] + A’C = AB.1 + A’C C+C’=1 = AB + A’C AB.1=AB

B

A

C

AB

A’C

F=AB+A’C

INPUT OUTPUT

A B C AB A’ A’C F=AB+A’C

0 0 0 0 1 0 0

0 0 1 0 1 1 1

0 1 0 0 1 0 0

0 1 1 0 1 1 1

1 0 0 0 0 0 0

1 0 1 0 0 0 0

1 1 0 1 0 0 1

1 1 1 1 0 0 1

Circuit Simplification Using Karnaugh MapExample 1 Boolean Function F=ABC + ABC’ + A’C

ABCA

F = ABC + ABC’ + A’C

BC

ABC’

A’C

INPUT OUTPUT

A B C ABC C’ ABC’ A’ A’C F=ABC+ABC’+A’C

0 0 0 0 1 0 1 0 0

0 0 1 0 0 0 1 1 1

0 1 0 0 1 0 1 0 0

0 1 1 0 0 0 1 1 1

1 0 0 0 1 0 0 0 0

1 0 1 0 0 0 0 0 0

1 1 0 0 1 1 0 0 1

1 1 1 1 0 0 0 0 1

0 1

0 1

1 1

0 0

Step 1 : Place Input-Output values in table

ABC

00

01

11

10

0 1

Rectangle 1

A B C0 0 10 1 1

Product of Rectangle 1 : A’C

Because A and C are constant A’ because value of A is zero.C because value of C is one.

Rectangle 2

A B C1 1 01 1 1

Product of Rectangle 2: AB

Because A and Bare constant A because value of A is one.B because value of B is one.

Simplified Circuit using K-map = Rectangle 1 + Rectangle 2 = A’C + AB

Exercise Boolean Function F=A’B’C’ + A’B’C + AB’C’ + ABC’

1. Simplify circuit using boolean rules.2. Simplify circuit using Karnaugh Map.

Concept of Machine Level, Assembly Level and High Level Programming

Processor

Assembler

Machine Level Language

Assembly Level Language

High Level Language

Compiler

Machine Level LanguageMachine level language is a language for processor.Machine language is represented in binary code.Machine level language is processor specific.Assembly Level LanguageIt is hard to program in machine language.To solve this problem, assembly language is used.In assembly language, machine code is represented by Mnemonic code.Assembly language is processor specific.Assembler is a software to convert assembly language program in machine language.

High Level LanguageIt is hard to develop and maintain large application programs in assembly language.To solve this problem, higher level languages like C,C++ etc. are used.In assembly language, machine code is represented by Mnemonic code.Compiler is a software to convert high level program to machine language.