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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
Correct answer is option 'D'. Can you explain this answer?
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Which of the following expressions is in the sum-of-products (SOP) for...
Explanation:

In boolean algebra, the sum-of-products (SOP) form is a way to represent a logical expression using the logical operators AND and OR. The SOP form consists of multiple product terms (also known as minterms) that are combined using the OR operator.

Let's analyze each of the given options to determine which one is in SOP form:

a) (A B)(C D)
This expression is not in SOP form because it is a product of two terms (A B and C D) that are being multiplied together. In SOP form, these terms should be combined using the OR operator.

b) (A)B(CD)
This expression is also not in SOP form because it is a product of three terms (A, B, and CD) that are being multiplied together. In SOP form, these terms should be combined using the OR operator.

c) AB(CD)
This expression is not in SOP form because it is a product of two terms (AB and CD) that are being multiplied together. In SOP form, these terms should be combined using the OR operator.

d) AB CD
This expression is in SOP form because it consists of two product terms (AB and CD) that are combined using the OR operator. The OR operator is implicit when there is a space or no operator between two terms.

Therefore, the correct answer is option 'D' (AB CD) as it is the only expression that is in SOP form.

To summarize:
- Options a, b, and c are not in SOP form because they involve products of terms without the OR operator.
- Option d is in SOP form because it consists of multiple product terms (AB and CD) combined using the OR operator.
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Community Answer
Which of the following expressions is in the sum-of-products (SOP) for...
Becz rest of them are in product -of- sum (POS) form
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