**Digital Circuits Questions and Answers – Sum of Products and Products of Sum**

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Sum of Products and Products of Sum”.

**1. The logical sum of two or more logical product terms is called __________**

a) SOP

b) POS

c) OR operation

d) NAND operation

**Answer:**a

**Explanation:**The logical sum of two or more logical product terms, is called SOP (i.e. sum of product). The logical product of two or more logical sum terms, is called POS (i.e. product of sums).

**2. The expression Y=AB+BC+AC shows the _________ operation.**

a) EX-OR

b) SOP

c) POS

d) NOR

**Answer:**b

**Explanation:**The given expression has the operation product as well as the sum of that. So, it shows SOP operation. POS will be the product of sum terms.

**3. The expression Y=(A+B)(B+C)(C+A) shows the _________ operation.**

a) AND

b) POS

c) SOP

d) NAND

**Answer:**b

**Explanation:**The given expression has the operation sum as well as the product of that. So, it shows POS(product of sum) operation. SOP will be the sum of product terms.

**4. A product term containing all K variables of the function in either complemented or uncomplemented form is called a __________**

a) Minterm

b) Maxterm

c) Midterm

d) ∑ term

**Answer:**a

**Explanation:**A product term containing all K variables of the function in either complemented or uncomplemented form is called a minterm. A sum term containing all K variables of the function in either complemented or uncomplemented form is called a maxterm.

**5. According to the property of minterm, how many combination will have value equal to 1 for K input variables?**

a) 0

b) 1

c) 2

d) 3

**Answer:**b

**Explanation:**The main property of a minterm is that it possesses the value 1 for only one combination of K input variables and the remaining will have the value 0.

**6. The canonical sum of product form of the function y(A,B) = A + B is __________**

a) AB + BB + A’A

b) AB + AB’ + A’B

c) BA + BA’ + A’B’

d) AB’ + A’B + A’B’

**Answer:**b

**Explanation:**A + B = A.1 + B.1 = A(B + B’) + B(A + A’) = AB + AB’ + BA +BA’ = AB + AB’ + A’B = AB + AB’ + A’B.

**7. A variable on its own or in its complemented form is known as a __________**

a) Product Term

b) Literal

c) Sum Term

d) Word

**Answer:**b

**Explanation:**A literal is a single logic variable or its complement. For example — X, Y, A’, Z, X’ etc.

**8. Maxterm is the sum of __________ of the corresponding Minterm with its literal complemented.**

a) Terms

b) Words

c) Numbers

d) Nibble

**Answer:**a

**Explanation:**Maxterm is the sum of terms of the corresponding Minterm with its literal complemented.

**9. Canonical form is a unique way of representing ____________**

a) SOP

b) Minterm

c) Boolean Expressions

d) POS

**Answer:**c

**Explanation:**Boolean Expressions are represented through canonical form. An example of canonical form is A’B’C’ + AB’C + ABC’.

**10. There are _____________ Minterms for 3 variables (a, b, c).**

a) 0

b) 2

c) 8

d) 1

**Answer:**c

**Explanation:**Minterm is given by 2

^{n}. So, 2

^{3}= 8 minterms are required.

**11. _____________ expressions can be implemented using either (1) 2-level AND-OR logic circuits or (2) 2-level NAND logic circuits.**

a) POS

b) Literals

c) SOP

d) POS

**Answer:** c

**Explanation:** SOP expressions can be implemented using either (1) 2-level AND-OR logic circuits or (2) 2-level NAND logic circuits.

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