# Find sum of minterm

#### CSharpque

Joined Sep 23, 2011
40
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?

#### CSharpque

Joined Sep 23, 2011
40
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.

#### aceminer

Joined Aug 26, 2011
21
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

#### Georacer

Joined Nov 25, 2009
5,182
@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.

#### CSharpque

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

#### Georacer

Joined Nov 25, 2009
5,182
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?

#### CSharpque

Joined Sep 23, 2011
40
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:

#### Georacer

Joined Nov 25, 2009
5,182
Your truth table is correct. A bare and easy to read version of it would be:
Rich (BB code):
X Y Z F
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1
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?