# which of the following expressions is in the sum-of-products form?

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## Which of the following expressions is in the sum

Click here👆to get an answer to your question ✍️ Which of the following expressions is in the sum - of - products (SOP) form?

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

Easy Open in App Solution Verified by Toppr

Correct option is D)

Among the options In option:[D]

AB and CD are in the form of products.

So, AB+CD is in the form of sum-of-products.

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## Which of the following expressions is in the sum

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. Ans: Hint: In this question, we have to check all the four options which are given in the question to check which expressio...

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 Verified 181.5k+ views 1 likes

**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) (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 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 isAB+CD. 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.

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## [Solved] Which of the following expressions is in the Sum

The correct answer is option 4. Concept: Sum of Product: SOP is an abbreviation for Sum of Product. Sum of product form is a Boolean algebra statement in whi

Home Digital Electronics Logic Gates and Boolean Algebra Representation of Boolean Functions SOP Form

## Question

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## Which of the following expressions is in the Sum-Of-Products (SOP) form?

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(A + B)(C + D) (A)-B (CD) AB (CD) AB + CD

## Answer (Detailed Solution Below)

Option 4 : AB + CD

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## Detailed Solution

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The correct answer is **option 4.**

**Concept:**

**Sum of Product:**

SOP is an abbreviation for Sum of Product. Sum of product form is a Boolean algebra statement in which distinct product terms of inputs are added together. This product is not an arithmetic multiply, but rather a Boolean logical AND, with the Sum being a Boolean logical OR.

SOP gives a minterm of a logical expression.

**Example:**

F= XY+YZ+ XZ

The above expression can be written like,

F= X.Y+Y.Z+ X.Z

F= (X) and (Y) or (Y) and (Z) or (X) and (Z)

**In minterms X takes as '1' and X' takes 0 similarly same conventions follow for all variables.**

XY= 110 (m6) and 111 (m7)

YZ= 011 (m3) and 111 (m7)

ZX= 101 (m5) and 111 (m7)

Min terms are, F= Σ(3,5,6,7)

**Product of sum:**

POS is an abbreviation for Product of Sum. Product of sum form is a Boolean algebra statement in which distinct product terms of inputs are multiplied together. This Sum is a Boolean logical OR, with the product being a Boolean logical AND.

POS gives a maxterm of a logical expression.

Example:

F= (X+Y). (Y+Z). (X+Z)

The above expression can be written like,

F= X+Y). (Y+Z). (X+Z)

F= (X) or (Y) and (Y) or (Z) and (X) or (Z)

In max terms X takes as '0' and X' takes '1' similarly same conventions follow for all variables.

X+Y= 000 (M0), 001 (M1)

Y+Z=000 (M0), 100 (M4)

Z+X=000 (M0), 010 (M2)

Max terms are, F= Σ(0, 1, 2,4)

**Option 1:(A + B)(C + D)**

**False**, It is in product of sum.

**Option 2:(A)-B (CD)**

**False,**It is not in POS and SOP.

**Option 3: AB (CD)**

**False**, It is not in POS and SOP.

**Option 4: AB + CD**

**True**, It is a correct form Sum of Product. It is Boolean logical AND, with the Sum being a Boolean logical OR.

**Hence the correct answer is**AB+CD.

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## More Representation of Boolean Functions Questions

**Q1.**Which of the following expressions is in the Sum-Of-Products (SOP) form?

**Q2.**The simplified SOP (Sum of Product) form of the Boolean expression (P + Q̅ + R̅)⋅(P + Q̅ + R)⋅(P + Q + R̅) is

**Q3.**A + AB gets simplified to:

**Q4.**Assume x' represents negation of x the Boolean function x'y' + xy + x'y is equivalent to?

**Q5.**The Boolean SOP expression obtained from the truth table is: Inputs Output A B C X 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0

**Q6.**In K-map reduction for 4-variables POS expression, the cell with address 0000 indicates:

**Q7.**The product of sum expression of a Boolean function F(A, B, C) of three variables is given by F(A, B, C) = ( A + B + C̅) ∙ (A + B̅ + C̅) ∙ ( A̅+ B + C ) ∙ ( A̅+ B̅ + C̅) The canonical sum of product expression of F(A, B, C) is given by

**Q8.**The minterm expansion of f (P, Q, R) = PQ + QR̅ + PR̅ is

**Q9.**Which one of the following gives the simplified sum of products expression for the Boolean function F = m0 + m2 + m3 + m5, where m0, m2, m3 and m5 are minterms corresponding to the inputs A, B and C and A as the MSB and C as the LSB?

## More Logic Gates and Boolean Algebra Questions

**Q1.**For a three input NOR gate, the possible number of states where output is 0 equals:

**Q2.**In a logic gate output will be 1 if:

**Q3.**The Boolean simplified form for S = (X + Y) (X + Z) is _______.

**Q4.**If function f(X, Y, Z) = ∑ m(2, 3, 4, 5) is implemented using SOP form, the resultant Boolean function would be _________.

Guys, does anyone know the answer?