Question

Given the function F (X, Y , Z)=Σm(0,1, 2 , 4 , 6) answer the following questions: 1. Obtain the expression in the Canonical Disjunctive Normal Form 2. Obtain the expression in the Canonical Conjunctive Normal Form 3. Derive the truth table for both the Minterms and Maxterms 4. Obtain the minimized SOP and POS 5. Draw the resultant circuit diagram for the minimized SOP

Answer 1

Given the function F (x, y, z)=Σm(0,1, 2 , 4 , 6) answer the following questions:

1. Obtain the expression in the Canonical Disjunctive Normal Form

$F(x,y,z) = \bar x \bar y \bar z + \bar x \bar y z + \bar x y \bar z + x \bar y \bar z + x y \bar z$

2. Obtain the expression in the Canonical Conjunctive Normal Form

$F(x,y,z) = (x + \bar y + \bar z)(\bar x + y + \bar z)(\bar x + \bar y + \bar z)$

3. Derive the truth table for both the Minterms and Maxterms

4. Obtain the minimized SOP and POS

Let's receive (from POS) minimized SOP:

$F(x,y,z) = (x + \bar y + \bar z)(\bar x + y + \bar z)(\bar x + \bar y + \bar z) = \newline \Big[ (a + b)(a + \bar b) = aa + a \bar b + ab + b \bar b = a + a(\bar b + b) + F = a + aT = a + a = a \Big] = \newline (x + \bar y + \bar z)(\bar x + \bar z) = x \bar x + x \bar z + \bar x \bar y + \bar y \bar z + \bar x \bar z + \bar z \bar z = \bar z + \bar z (x + \bar x) + \bar x \bar y + \bar y \bar z = \newline \bar z + \bar z T + \bar z \bar y + \bar x \bar y = \bar z (T + T + \bar y) + \bar x \bar y = \bar z + \bar x \bar y$

Equivalent minimized POS will be:

$\bar z + \bar x \bar y = (\bar z + \bar x)(\bar z + \bar y)$

5. Draw the resultant circuit diagram for the minimized SOP