Improve company productivity with a Business Account.Sign Up

x
?
Solved

Needs help in problem

Posted on 2011-09-16
5
Medium Priority
?
655 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
  • 3
5 Comments
 
LVL 18

Accepted Solution

by:
deighton earned 1000 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 1000 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

What Kind of Coding Program is Right for You?

There are many ways to learn to code these days. From coding bootcamps like Flatiron School to online courses to totally free beginner resources. The best way to learn to code depends on many factors, but the most important one is you. See what course is best for you.

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.

Join & Write a Comment

Article by: Nadia
Linear search (searching each index in an array one by one) works almost everywhere but it is not optimal in many cases. Let's assume, we have a book which has 42949672960 pages. We also have a table of contents. Now we want to read the content on p…
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
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.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

580 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