modulo division

8/10/2019 Modulo Division

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1/11/2015 1EED, NIT Calicut


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If x is a non negative integer and y is a positiveinteger then we define x mod y to be theremainder when x is divided by y

x mod y= remainder(x/y)=x-int(x/y)*y It will be an integer from the set {0 1 2 3 4 5 6 7 8

9..y-1}

1/11/2015 EED, NIT Calicut 2


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What day of the week will be 21 March 2012?



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21 March 2011 is MONDAY There are 365 days in a regular year 7 days after 21.03.2011 is Monday

14 days after 21.03.2011 is Monday

Like that, 7n days after 21.03.2011 is Monday

So we find 365 mod 7



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We get answer as 1 This means

If the year not a leap year, 21 March 2012 could

have been Tuesday

But year2012 is a Leap year

So 21.03.2012 shall be Wednesday



7/321/11/2015 EED, NIT Calicut 7


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ISBN is International Standard Book Number There are two systems now in practice ISBN 10 and ISBN 13

ISBN 10 uses a 10 characters four field string ISBN 13 uses a 13 characters five field string Only decimal digits are used in the character string

From 1 January, 2007 , an ISBN consists of 13 digitspreceded by the letters ISBN.



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Find the sum s=first digit x1 + second digit x 2 +third digit x 3 +.+ninth digit x 9

Then Check code=s mod 11

Eg. ISBN 81-203-0884-0 S=8+1*2+2*3+0*4+3*5+0*6+8*7+8*8+4*9 S=187

CC=187 mod 11=0 81-203-0884-0



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ISBN 13 is a new code system introduced by ISO in2007

It has thirteen character five field string with last

field as the check code Field 1 Code for industry(978 or 979 for book publishing

industry)

Field 2 Area code /Group code

Field 3 Publisher Code Field 4 -Book Code

Field 5 Single digit Check Code



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The check code is calculated as follows Each of the first 12 digits of the ISBN is alternately

multiplied by 1 and 3.

The check digit is equal to 10 minus the remainderresulting from dividing the sum of the weightedproducts of the first 12 digits by 10 with one

exception. If this calculation results in an apparent check digit

of 10, the check digit is 0.



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ISBN 978- 0-070-60168-0 ISBN 979-81-77-58358-7



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0 or 1 for English 2 for French 3 for German

4 for Japan 5 for Russia 7 for China

81 for India 9971 for Singapore .



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Raja Rammohun Roy National Agency for ISBN

Ministry of HRD

A2/W4, Curzon Road Barracks,

Kasturba Gandhi Marg,

New Delhi-110001

Telephone No. 23384687, 23382549 (Extn. 12)



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Cryptology is the science of encrypting anddecrypting messages for maintaining informationsecurity



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Caesar encryption method can be represented bythe function f that assigns to the non negativeinteger p, p25 with f(p)=(p+3) mod 26



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Code the word SECRET using Caesar method



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{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z} {0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

22 23 24 25}



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{

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

0 1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25


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Original Message is obtained from the secret codeusing decryption using

f -1 =(p-3)mod 26

This is only a simple method of encryption, whichcan be easily hacked

There are several algorithms for encrypting

messages



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PRN is a sequence of numbers which shows certaindegree of statistical independence required for arandom number sequence

But it is not purely random. So we call it as pseudo random sequence



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PRN can be generated on the computer usingseveral techniques

The Linear Congruential method is very popular

That is, we generated a sequence of pseudorandom numbers {xn} with 0xn


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x0is called the seed It is seen that m=231-1, a=75, c=0 Then m=2,147,483,647

And a=16807 This sequence about 2147 million random numbers



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Use m=9, a=7, c =4, and x0=3 and generate the first12 random numbers



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

We find that the sequence gets repeated after 9

numbers, which is the period length of the PRNsequence for m=9

This repetition happens for any PRN sequence for a

given m, a and x0



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Hashing is the process of mapping a key to amemory location based on the Hash valuecalculated for the Key using a Hash function

One of the method of Hash function uses theModulo mdivision technique in which the result ofthe Modulo division gives the location/address of

the Key in the HASH TABLE

modulo division

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