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Que. The simplified SOP (Sum Of Product) form of the boolean expression (P + Q' + R') . (P + Q' + R) . (P + Q + R') is
a. (P'.Q + R')
b. (P + Q'.R')
c. (P'.Q + R)
d. (P.Q + R)
Answer:(P + Q'.R')
QAISAR AZIZ SHAHZAD :(August 27, 2019) xample

Convert the following Boolean function into Standard PoS form.

f = (p + q + r).(p + q + r’).(p + q’ + r).(p’ + q + r)

The given Boolean function is in canonical PoS form. Now, we have to simplify this Boolean function in order to get standard PoS form.

Step 1 − Use the Boolean postulate, x.x = x. That means, the Logical AND operation with any Boolean variable ‘n’ times will be equal to the same variable. So, we can write the first term p+q+r two more times.

⇒ f = (p + q + r).(p + q + r).(p + q + r).(p + q + r’).(p +q’ + r).(p’ + q + r)

Step 2 − Use Distributive law, x + (y.z) = (x + y).(x + z) for 1st and 4th parenthesis, 2nd and 5th parenthesis, 3rd and 6th parenthesis.

⇒ f = (p + q + rr’).(p + r + qq’).(q + r + pp’)

Step 3 − Use Boolean postulate, x.x’=0 for simplifying the terms present in each parenthesis.

⇒ f = (p + q + 0).(p + r + 0).(q + r + 0)

Step 4 − Use Boolean postulate, x + 0 = x for simplifying the terms present in each parenthesis

⇒ f = (p + q).(p + r).
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