# Find sum of minterm

Discussion in 'Homework Help' started by CSharpque, Sep 23, 2011.

1. ### CSharpque Thread Starter Member

Sep 23, 2011
40
0
hello
I have one difinition
Obtain the truth table of following functions and express the function in sum of minterms and product of maxterm

(xy+y)(y+xz)

Solution:-

Truth Table

x y z
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

i known how to create turth table n i have create it as above.
now how to find minterm? i don't known plz explain this question?

Nov 25, 2009
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1,266
3. ### CSharpque Thread Starter Member

Sep 23, 2011
40
0
There was no truth table given in definition. Definition is only the characters which are bold in my post. TRUTH TABLE IS CREATED BY ME AS I UNDERSTAND.

4. ### aceminer New Member

Aug 26, 2011
21
0
Well the sum of minterms should be z and the product of sum should be z'... Pardon me if I am wrong as I am also new to this topic... But I did it using k maps method based on your truth table

5. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
@CSharpque

You are given a Boolean logic function F=(xy+y)(y+xz). That function is TRUE for some combinations of x,y,z and FALSE for some others. It is your job to use the truth table that has all of the x,y,z combinations and tell for which ones F is TRUE and for which it is FALSE. You usually and an extra column after the x,y,z combinations where you write 1 or 0, if F is TRUE of FALSE respectively for that combination.
See that table as an example: http://www.kollewin.com/EX/09-15-17/truth_table.jpg

Please post a complete truth table.

@aceminer

It is nice to want to help a fellow member, but here in the Homework Help forum we have a policy of not giving the OP the answer right away, but try to guide him to find the solution by himself. Keep that in mind for future occurrences.

6. ### CSharpque Thread Starter Member

Sep 23, 2011
40
0
THere is no truth table given in definition. That table is created by me as i understand.

7. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Yes, that is correct. I ask you to post the truth table of the function F=(xy+y)(y+xz). It is vital for you to proceed.

After you do that make a Karnaugh map with that table and minimize it. Do you know how?

8. ### CSharpque Thread Starter Member

Sep 23, 2011
40
0
yes i know n that is
X Y Z Xy Xz Xy+y Y+xz (xy+y)(y+xz)
0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 0 0 0 1 1 1
0 1 1 0 0 1 1 1
1 0 0 0 0 0 0 0
1 0 1 0 1 0 1 0
1 1 0 1 0 1 1 1
1 1 1 1 1 1 1 1
am i right?

Last edited: Sep 27, 2011
9. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Your truth table is correct. A bare and easy to read version of it would be:
Code ( (Unknown Language)):
1.
2. X Y Z F
3. 0 0 0 0
4. 0 0 1 0
5. 0 1 0 1
6. 0 1 1 1
7. 1 0 0 0
8. 1 0 1 0
9. 1 1 0 1
10. 1 1 1 1
11.
The minterms of the function F are those combinations of XYZ that satisfy the function. From the truth table we see that F is true for {XYZ}={010,011,110,111}.

In Boolean terms, these combinations correspond to the terms {X'YZ',X'YZ,XYZ',XYZ}. If you replace the combinations from the previous bracket to the terms in the last bracket, all of them will produce 1 (or TRUE).

That is why the function F can be re-written as the sum of its minterms:
F=X'YZ'+X'YZ+XYZ'+XYZ.
Any combination of inputs that should give F=TRUE, based on the truth table, will satisfy the above Sum of Products expression.

Is that clear?

CSharpque likes this.
10. ### CSharpque Thread Starter Member

Sep 23, 2011
40
0
thanks for help. i get the answer and understand perfectly..