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Posted on 2011-09-16
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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
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Question by:mustish1
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5 Comments
 
LVL 18

Accepted Solution

by:
deighton earned 250 total points
Comment Utility
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
Comment Utility
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
Comment Utility
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
Comment Utility
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
Comment Utility
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
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