Solved

Needs help in problem

Posted on 2011-09-16
5
567 Views
Last Modified: 2012-05-12
Hi guys: Can any one please help me in that problem. I dont understand how this table is created ? Thanks.


Compute the following airthmetic problems in Z/8. Represent answer with the least positive representative of the appropriate equivalence class.

a. [3] + [7]
b. [2] . ([4] + [5])



Addition and multiplication tables for Z/6.
----------------------------------------------------
+  0  1  2  3  4  5
0  0  1  2  3  4  5
1  1  2  3  4  5  0
2  2  3  4  5  0  1
3  3  4  5  0  1  2
4  4  5  0  1  2  3
5  5  0  1  2  3  4

x  0  1  2  3  4  5
0  0  0  0  0  0  0
1  0  2  3  4  5  0
2  0  2  4  0  2  4
3  0  3  0  3  0  3
4  0  4  2  0  4  2
5  0  5  4  3  2  1
0
Comment
Question by:mustish1
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 3
5 Comments
 
LVL 18

Accepted Solution

by:
deighton earned 250 total points
ID: 36550210
what you have to do is calculate the value as normal, but then to change into Z/6
you divide by 6 and take the remainder

e.g.

5 x 5 = 25

25 divided by 6 = 4 remainder 1

you only need the '1', as in the table

although some of the values in the 'x' table look wrong, for example 1 x 1 = 1 , not 2 as in the table

_____________________

note also your question asks for z/6, but your tables are z/6

so for z/8, work out then divide by 8, and keep the remainder
0
 

Author Comment

by:mustish1
ID: 36551038
x  0  1  2  3  4  5
0  0  0  0  0  0  0
1
2
3
4
5

i try. In the case of multiplication ist row is all zero:
0*0 =0

in 2nd row. Can you please tell me one more time the second row in the multiplication case
0
 

Author Comment

by:mustish1
ID: 36552804
x  0  1  2  3  4  5
0  0  0  0  0  0  0
1  0  1  2  3  4  5
2  0  2  4  0  2  4
3  0  3  0  3  0  3
4  0  4  2  0  4  2
5  0  5  4  3  2  1

0
 

Author Comment

by:mustish1
ID: 36552814
x  0  1  2  3  4  5
0  0  0  0  0  0  0
1  0      3
2
3
4
5

For 2nd row
1*0 = 0/6 =0
1*1 = 1/6 =
1*2 = 2/6 = 3 reminder
1*4 = 4/6  =  1 reminder
1*5 = 5/6  =  1 reminder

I made mistake
0
 
LVL 31

Assisted Solution

by:GwynforWeb
GwynforWeb earned 250 total points
ID: 36554217
This script calculates the tables, (just copy into Notepad, save as .htm and open in browser)

<script>
n=6;
for (i=0;i<n;i++){
   for (j=0;j<n;j++)
     document.write( (i*j)%n  + " ")
   document.write("<br>");
}
</script>

 Here are the results for n= 6, your table is correct

0 0 0 0 0 0
0 1 2 3 4 5
0 2 4 0 2 4
0 3 0 3 0 3
0 4 2 0 4 2
0 5 4 3 2 1

to get the + table just change i*j to i+j

Any arithmetic mod 6 is simply the remainder after dividing by 6
Note you can add as many 6's as you like when do arithmetic mod 6, as  6 mod 6 = 0  

Be careful with negatives though.

eg  

(2 - 4 ) mod 6 = - 2     now add 6 onto it give 4 ie the least +ve result,

(3 -2*5) mod 6 = -7 mod 6 = -1    now add 6 to give the least +ve result 5
0

Featured Post

Technology Partners: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
Okay. So what exactly is the problem here? How often have we come across situations where we need to know if two strings are 'similar' but not necessarily the same? I have, plenty of times. Until recently, I thought any functionality like that wo…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

635 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question