# Truth Tables/Minimizing/SOP/POS Part 2

#### shamieh

##### Active member
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) = $$\displaystyle \sum$$m(0,1,2,6,7)

1. x y z | f
2. 0 0 0 |1
3. 0 0 1 |1
4. 0 1 0 |1
5. 0 1 1 |0
6. 1 0 0 |0
7. 1 0 1 |0
8. 1 1 0 |1
9. 1 1 1 |1

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

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)

• 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