Computer Hardware & Software - Session 3 pps

Session Objectives Describe what a Number system is  Explain the decimal, octal and hexadecimal number systems  Convert a number from one number system to another  Practice binary ar

Data Representation in Computers/Session 3 / 1 of 45

Data Representation in

Computers

Session 3

Session Objectives

 Describe what a Number system is

 Explain the decimal, octal and hexadecimal number systems

 Convert a number from one number system

to another

 Practice binary arithmetic

 List the various standard codes used to

represent the unit of information

– ASCII

– EBCDIC

Session Objectives (Contd.)

Number systems

earlier consisted of symbols e.g

Roman number system - I for 1,

II for 2, III for 3 etc

represent different values depending

on the position they occupy e.g the

Decimal system

Decimal Number System

successive position to the left of

the decimal point represent units,

tens, hundreds, thousands etc

its value

therefore are called positional

number system

Base

Position number

(6*10)

Decimal Number System

(Contd.) The value of each digit in the

number system is determined by:

a) The digit itself

b) The position of the digit

in the number

c) The base/radix of the system

Binary Number System

and symbols used are 0 and 1

the value of the digit will be two times greater than its predecessor because the base is two

0001111001010111

Least Significant bit Most Significant bit

Binary Number

Octal number systems Binary Octal

Octal Number System

increase from right to left as 1, 8, 64, 512,

4096

be computed as :

1204 = (1 * 512) + (2 * 64) + (0 * 8) + (4 * 1) = 512 + 128 + 0 + 4

= 644

Octal Number System

Binary Octal

0000 0011 0102 0113

100 4 1015

110 6

111 7

 To convert a number from binary to octal and vice versa, the following table must be kept in mind:

Hexadecimal Number

Systems

Hexadecimal Decimal

0 0

1 1

2 2

3 3

4 4

5 5

6 6

7 7

8 8

9 9

A 10

B 11

C 12

D 13

E 14

F 15

Hex Number Systems(Contd.)

 Uses a base of 16

hexadecimal number system obtained

by using the alphabets A, B, C,

D, E and F

decimal equivalent of a hexadecimal

Converting binary numbers to decimal

 Divide the decimal number by the

base of the required number system

and divide the quotient again with the base

 Keep repeating this process until quotient is reduced to a zero

order gives the binary equivalent

Decimal to Binary

Conversion

E.g Converting the decimal number 52

to its binary equivalent.

Binary to Hexadecimal

 Each hexadecimal digit is represented

by 4 binary digits.

Binary Hexadecimal

0000 0

0001 1

0010 2

0011 3

0100 4

0101 5

0110 6

0111 7

1000 8

1001 9

1010 A

1011 B

1100 C

1101 D

1110 E

1111 F

Binary to Hexadecimal

(Contd.)

Split the quantity into groups of four

outwards from right to left

Each group of four is directly converted into its hexadecimal equivalent

Add zeros to the left of the number if

Hexadecimal to

Binary

hexadecimal digit in groups of four

Converting from Binary to Octal

 The binary number must be

divided into groups of three from

the octal point- to the right in case

of the fractional portion and to the

left in case of the integer portion

 Each group can then be replaced

with their octal equivalent

 We may add zero to the left of the

number if required.

For example : Binary 101010101010100

101 010 101 010 100

5 2 5 2 4

 52524 is the octal equivalent of the given binary number.

Converting from Octal to Binary

 Each octal digit is replaced with the appropriate

‘triple’ of binary digits.

Binary Concepts

OFF ON

DATA (in binary Digits)

printf(“ Hello”);

printf(“We are enjoying a world

of alphabetical coding”);

}

Data Representation

 Byte is a sequence of 8 bits

consist of 8 or 16 bits

per word could be 16 or 32 bits

Data representation

(Contd.)

is converted to a binary character

code and transmitted to the computer

 Each character to the printer, screen,

disk is communicated in binary code

 While displaying or printing, the character

is converted back to human readable form

 Data is stored and processed in computers in the binary form These symbols 0 and 1, are called bits

i.e 00, 01, 10 , 11

 A string of 8 bits is called a byte

Data Storage

 During calculation the decimal number

is converted to its binary equivalent.

 After calculation the result is converted back to its decimal equivalent.

Data Storage (Contd.)

The Packed

Decimal

 Packed decimal - data is stored in

a half- way house between pure binary

and one byte per digit

 Four bits are required to store all 10

symbols that constitute the decimal

number system

of two decimal digits

e.g The number 34 would be stored

in character form as:

Byte 1 Byte 2

00000011 00000100

3 4 Using packed decimal the same number

Binary Arithmetic Addition

The following rules of binary addition

Complementary

Subtraction

Three steps to perform subtraction :

subtracting

number we are subtracting from

 If there is a carry of 1 add the carry to the result of the addition

else

re-complement the sum and attach a negative sign

To find the complement of a binary

number invert all the bits

Step 2 Add the number you are

Complementary Subtraction

(Contd.)

Step 3 Since there is no carry we

re-complement the result and add a negative sign

Thus the answer is -10111001

Complementary Subtraction

(Contd.)

Divisio n

1 Start from the left of the dividend

2 Perform subtraction i.e divisor should be subtracted from the dividend

a) if subtraction is possible put 1 in the

quotient and subtract the divisor

from digits of the dividend

else

put 0 in the quotient

b) bring down the next digit to the

right of the remainder

3 Do step 2 till no more digits remain in

the dividend

Divisio n

The complete table for binary division is:

0/1 = 0 1/1 = 1 For example:

100001 / 110 Then,

Unit of Information

binary numbers to represent letters, special symbols, decimal numbers etc

 7 digits are required to uniquely represent all 128 characters

of data between computers

ASCI I

Code for Information Interchange (ASCII)

ASCII uses 7 bits per character

possible to provide 128 different

arrangements

end of file, end of page etc to the computer

control characters

internally in personal computers

EBCDI C

Interchange Code ( EBCDIC)

using EBCDIC

mainframe models and other similar

machines

 Electronic Circuits available to transform characters from ASCII to EBCDIC and

vice- versa

using a computer program

An insight into CPU

 CPU also referred, as Microprocessor is actually the brain of a computer

 There are lot of chips on the motherboard and they all kind of look alike

 There are several companies who

manufacture microprocessor chips :

Advanced Micro Devices (AMD),

Cyrix, Intel …

CPU Properties

The following are some of CPUs properties:

What is meant by CPU speed?

 Every computer contains an internal clock that regulates the rate at which each instruction is executed

 The clock speed is measured in terms of MegaHertz (MHz)

 1 Mhz is equal to 1 million cycles per second Hence a computer with 120 MHz speed means

120 million cycles per second

 It must be noted that a faster CPU with less hard disk space would result into a mediocre machine performance.

What if I increase the speed of clock?

the speed for which it has been tested and approved is also called as “Overclocking”

faster by setting the jumper on the motherboard But it may cause overheating

damage the chip but the computer would not function properly

What is meant by Word Size and

how is it related with speed?

workbenches These workbenches are called as registers

the CPU All data must be represented in the register before it can be processed

each (in terms of bits) determine the speed and performance of the CPU

operation is determined by size of a word