Question

Which of the following expressions is in the sum-of-products (SOP) form?
(a) (A + B) (C + D)
(b) (A)B(CD)
(c) AB(CD)
(d) AB + CD

Answer 1

Hint: In this question, we have to check all the four options which are given in the question to check which expression is in the form of SOP. First, eliminate the options which do not have the additional operative, then with the remaining options, find the expression which is SOP (Sum of products) according to the explanation of the required form.

Complete step-by-step solution
We have to find which of the following expressions from the given options are in the form of SOP or sum-of-products.
Since it mentions the sum in SOP, we only need to concentrate on the options which have the operative ‘+’ in the expression. Therefore, if we see the given options, we can see that the option (a) and option (d) have the mathematical operative ‘+’ in their expression.
Now, after narrowing it down to two options, let us check which one of these expressions is in the sum of products (SOP) form.
For option (a):
$(A + B) (C + D)$
This option is in the form of POS, which is also known as the product of sums, which will give the product of two different additions.
For option (b):
$AB + CD$
The option above is in the form of SOP, Sum of products, which will give the sum of the two different multiplications.
Hence, the expression which is in the form of SOP is $AB + CD.$

Note: Here, the two forms we found were POS and SOP which are the two types of the canonical expression. The canonical expression can be defined as a Boolean expression which has either a minterm or max term.