Can anyone check my answers? I need help on the last one as well. Wasn't sure if anyone remembered or knew how to do this. thought I'd give it a try tho. here is the forum I originally posted on, that way I dont have to retype [url="http://http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/truth-tables-minimizing-sop-pos-part-2-a-6517.html"]My Boolean Problem [/url]

## 2 Replies - 4136 Views - Last Post: 20 September 2013 - 07:13 AM

### #1

# Boolean Algebra/Sum of Products/Products of Sums/Truth Table

Posted 19 September 2013 - 08:35 PM

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**Replies To:** Boolean Algebra/Sum of Products/Products of Sums/Truth Table

### #3

## Re: Boolean Algebra/Sum of Products/Products of Sums/Truth Table

Posted 20 September 2013 - 07:13 AM

It would actually be really helpful if you did post your problem here. That way, the question is here for others who visit this thread in the future.

The question:

The question:

Quote

Need someone to check my answers once more. (Promise this is the last time lol)

Draw the truth table corresponding to f(X,Y,Z) = ∑m(0,1,2,6,7)

Answer:

x y z | f

0 0 0 |1

0 0 1 |1

0 1 0 |1

0 1 1 |0

1 0 0 |0

1 0 1 |0

1 1 0 |1

1 1 1 |1

Write out the canonical sum of products SOP expression for f(X,Y,Z) of problem above.

ANSWER:

x!y!z! + x!y!z + x!yz! + xyz! + xyz

Minimize the expression above.

x!y!z!+x!y!z+x!yz!+xyz!+xyz = x!y!(z! + z) + y(x!z! + xz! + xz) --->

= y[z!(x! + x) + xz] = (x! + x) + xz = 1 + xz = x!y! + xz?

Draw the truth table corresponding to f(X,Y,Z)= POSM(1,2,3) (product of sums symbol M)

ANSWER:

x y z | f

0 0 0 |1

0 0 1 |0

0 1 0 |0

0 1 1 |0

1 0 0 |1

1 0 1 |1

1 1 0 |1

1 1 1 |1

write out the canonical sums POS expression for $f(x,y,z) of the prob above.

ANSWER:

(x + y + z!)(x + y! + z)(x + y! + z!)

minimize the expression...

Just need someone to check my answers and help me solve the last problem.

Don't know how to minimize it when I can't factor it out. I also have 9 terms.. So I need to distribute it?

HELP

thank you.

Sham

Draw the truth table corresponding to f(X,Y,Z) = ∑m(0,1,2,6,7)

Answer:

x y z | f

0 0 0 |1

0 0 1 |1

0 1 0 |1

0 1 1 |0

1 0 0 |0

1 0 1 |0

1 1 0 |1

1 1 1 |1

Write out the canonical sum of products SOP expression for f(X,Y,Z) of problem above.

ANSWER:

x!y!z! + x!y!z + x!yz! + xyz! + xyz

Minimize the expression above.

x!y!z!+x!y!z+x!yz!+xyz!+xyz = x!y!(z! + z) + y(x!z! + xz! + xz) --->

= y[z!(x! + x) + xz] = (x! + x) + xz = 1 + xz = x!y! + xz?

Draw the truth table corresponding to f(X,Y,Z)= POSM(1,2,3) (product of sums symbol M)

ANSWER:

x y z | f

0 0 0 |1

0 0 1 |0

0 1 0 |0

0 1 1 |0

1 0 0 |1

1 0 1 |1

1 1 0 |1

1 1 1 |1

write out the canonical sums POS expression for $f(x,y,z) of the prob above.

ANSWER:

(x + y + z!)(x + y! + z)(x + y! + z!)

minimize the expression...

Just need someone to check my answers and help me solve the last problem.

Don't know how to minimize it when I can't factor it out. I also have 9 terms.. So I need to distribute it?

HELP

thank you.

Sham

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