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Unit 2: Boolean Algebra and Logic gates - Practice Quiz

ECE213 — Digital Electronics 60 Questions
0 Correct 0 Wrong 60 Left
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1 Which logic gate produces a HIGH output only when all its inputs are HIGH?

Logic Gates Easy
A. OR gate
B. NOR gate
C. NOT gate
D. AND gate

2 The output of a NOT gate is:

Logic Gates Easy
A. The product of the inputs
B. The sum of the inputs
C. The complement of the input
D. Always HIGH

3 Which gate is known as the universal gate along with NOR?

Logic Gates Easy
A. XOR gate
B. NAND gate
C. AND gate
D. OR gate

4 The XOR gate produces a HIGH output when:

Logic Gates Easy
A. Both inputs are HIGH
B. Both inputs are LOW
C. The inputs are equal
D. The inputs are different

5 For a logic function with input variables, how many rows does its truth table have?

Truth Table Easy
A.
B.
C.
D.

6 A truth table is used to:

Truth Table Easy
A. List all possible input combinations and their outputs
B. Simplify only using algebra
C. Convert decimal to binary
D. Draw only the gate symbols

7 According to Boolean algebra, the value of is:

Boolean Algebra Easy
A.
B.
C.
D.

8 The Boolean expression equals:

Boolean Algebra Easy
A.
B.
C.
D.

9 Which of the following correctly states De Morgan's first theorem?

Boolean Algebra Easy
A.
B.
C.
D.

10 The Boolean expression simplifies to:

Boolean Algebra Easy
A.
B.
C.
D.

11 A minterm is a product term that includes:

Canonical and Standard form Representation Easy
A. Only two variables
B. All variables of the function, each once
C. Only complemented variables
D. Only one variable

12 A canonical Sum of Products (SOP) form is a sum of:

Canonical and Standard form Representation Easy
A. Minterms
B. Maxterms
C. Constants
D. Literals only

13 A maxterm is represented as a:

Canonical and Standard form Representation Easy
A. Single literal
B. Sum (OR) of all variables
C. Product (AND) of all variables
D. Constant

14 SOP stands for:

SOP and POS Simplification Easy
A. Sum of Positions
B. Series of Products
C. Set of Products
D. Sum of Products

15 In a POS (Product of Sums) expression, the sum terms are combined using the:

SOP and POS Simplification Easy
A. XOR operation
B. OR operation
C. NOT operation
D. AND operation

16 A Boolean function in SOP form can be directly implemented using:

Implementation of Boolean Functions Easy
A. Only NOT gates
B. Only XOR gates
C. AND gates followed by an OR gate
D. OR gates followed by an AND gate

17 Which two-level gate structure is used to implement a POS expression?

Implementation of Boolean Functions Easy
A. AND-OR
B. NAND-NAND
C. OR-AND
D. NOT-OR

18 A Karnaugh map (K-Map) is mainly used to:

K-Map Easy
A. Generate clock signals
B. Simplify Boolean expressions
C. Store binary data
D. Convert decimal to hex

19 How many cells does a K-Map for variables contain?

K-Map Easy
A.
B.
C.
D.

20 A don't care condition in a K-Map is usually denoted by:

Don't Care Easy
A.
B.
C.
D.

21 Which single logic gate can be used to implement any Boolean function, and is therefore called a universal gate, when its output equals ?

Logic Gates Medium
A. AND
B. OR
C. XOR
D. NAND

22 The output of a 2-input XNOR gate is HIGH when:

Logic Gates Medium
A. Both inputs are LOW only
B. Exactly one input is HIGH
C. Both inputs are equal
D. Both inputs are HIGH only

23 A truth table for a Boolean function has input variables. How many rows will the complete truth table contain?

Truth Table Medium
A.
B.
C.
D.

24 A function outputs only for the rows and . Which function does this truth table represent?

Truth Table Medium
A.
B.
C.
D.

25 Simplify the Boolean expression .

Boolean Algebra Medium
A.
B.
C.
D.

26 According to De Morgan's theorem, is equal to:

Boolean Algebra Medium
A.
B.
C.
D.

27 Which of the following is the correct simplification of ?

Boolean Algebra Medium
A.
B.
C.
D.

28 A minterm of a Boolean function is a product term in which:

Canonical and Standard form Representation Medium
A. Only complemented variables are allowed to appear
B. Every variable appears exactly once, either complemented or uncomplemented
C. At least one variable appears in true form
D. Variables are combined using the OR operation exclusively

29 For a 3-variable function, the minterm corresponds to which product term?

Canonical and Standard form Representation Medium
A.
B.
C.
D.

30 If a function is expressed as for variables , then in maxterm form the same function is:

Canonical and Standard form Representation Medium
A.
B.
C.
D.

31 The Product of Sums (POS) form of a Boolean function is a logical:

SOP and POS Simplification Medium
A. OR of AND terms
B. AND of OR terms
C. OR of OR terms
D. AND of AND terms

32 Convert the expression into its simplified SOP form.

SOP and POS Simplification Medium
A.
B.
C.
D.

33 Which of the following statements about SOP and POS is correct?

SOP and POS Simplification Medium
A. A canonical POS uses minterms while a canonical SOP uses maxterms
B. SOP and POS forms can never represent the same Boolean function
C. A canonical SOP uses minterms while a canonical POS uses maxterms
D. Both canonical SOP and POS are always built entirely from minterms of the function

34 To implement the function using only NAND gates, the minimum number of 2-input NAND gates required is:

Implementation of Boolean Functions Medium
A. 5
B. 3
C. 4
D. 2

35 A two-level AND-OR logic circuit can be directly converted to an equivalent two-level circuit using only:

Implementation of Boolean Functions Medium
A. XOR gates
B. AND gates
C. NAND gates
D. OR gates

36 A POS (OR-AND) implementation can be replaced by a two-level circuit using only which universal gate?

Implementation of Boolean Functions Medium
A. NAND
B. XNOR
C. AND
D. NOR

37 In a 4-variable Karnaugh map, a group of 8 adjacent cells (an octet) eliminates how many variables from the resulting product term?

K-Map Medium
A. 3
B. 2
C. 1
D. 4

38 Why must adjacent cells in a Karnaugh map differ in the value of exactly one variable when moving horizontally or vertically?

K-Map Medium
A. Because the cells are arranged in Gray code order so that only one bit changes between neighbours, allowing valid grouping
B. Because it reduces the total number of cells needed in the map
C. Because binary counting order is used to label the rows and columns
D. Because it forces the output column to alternate between and

39 A K-map grouping of 4 cells for a 3-variable function results in a product term containing how many literals?

K-Map Medium
A. 0
B. 1
C. 3
D. 2

40 Don't-care conditions in a Karnaugh map are useful because they:

Don't Care Medium
A. Must always be treated as 1 to guarantee a valid output for every input
B. Can be treated as either 0 or 1 to form larger groups and achieve greater simplification
C. Represent inputs that force the function output to remain permanently at 0
D. Are ignored entirely and never influence how groups are formed on the map

41 Simplify the Boolean expression to its minimal form.

Boolean Algebra Hard
A.
B.
C.
D.

42 For , what is the minimal SOP expression using a K-map?

K-Map Hard
A.
B.
C.
D.

43 Given with don't cares , what is the simplest SOP?

Don't Care Hard
A.
B.
C.
D.

44 A 2-input gate outputs only when both inputs differ, and its output is then inverted. Which single gate is functionally equivalent to this description?

Logic Gates Hard
A. NAND gate
B. NOR gate
C. XOR gate
D. XNOR gate

45 Convert into its minimal SOP form for variables .

SOP and POS Simplification Hard
A.
B.
C.
D.

46 The function is expressed as a product of maxterms. Which is correct?

Canonical and Standard form Representation Hard
A.
B.
C.
D.

47 What is the minimum number of two-input NAND gates required to implement ?

Implementation of Boolean Functions Hard
A. 3
B. 2
C. 5
D. 4

48 For a 4-variable K-map, a prime implicant that is the only cover for some minterm is called what?

K-Map Hard
A. Non-essential prime implicant
B. Redundant prime implicant
C. Selective prime implicant
D. Essential prime implicant

49 Using the consensus theorem, simplify .

Boolean Algebra Hard
A.
B.
C.
D.

50 A 3-input function outputs when an odd number of inputs are . How many rows of its truth table have output ?

Truth Table Hard
A. 3
B. 5
C. 2
D. 4

51 Minimize .

SOP and POS Simplification Hard
A.
B.
C.
D.

52 For with , which minimal expression is valid?

Don't Care Hard
A.
B.
C. giving -type forms
D.

53 Which statement about the universality of NOR gates is correct?

Logic Gates Hard
A. A NOR gate can realize AND and OR but not NOT
B. A NOR gate can realize NOT and OR but not AND
C. A NOR gate alone can realize AND, OR, and NOT functions
D. A NOR gate can only realize the OR function

54 Apply DeMorgan's theorem to simplify .

Boolean Algebra Hard
A.
B.
C.
D.

55 To implement any arbitrary 3-variable Boolean function using a single multiplexer, how many selection lines and data inputs are needed?

Implementation of Boolean Functions Hard
A. 3 selection lines and 4 data inputs
B. 2 selection lines and 8 data inputs
C. 3 selection lines and 8 data inputs
D. 4 selection lines and 8 data inputs

56 The standard SOP form differs from the canonical SOP form in that standard SOP:

Canonical and Standard form Representation Hard
A. Allows product terms that are not full minterms
B. Cannot be simplified further
C. Uses only maxterms in the expression
D. Requires every term to contain all variables

57 In a 5-variable K-map, two mirrored cells across the axis of symmetry that hold the same value can be combined. What does such a combination eliminate?

K-Map Hard
A. The variable distinguishing the two map halves
B. The output variable
C. None of the input variables
D. Two variables simultaneously

58 A function of 4 variables has exactly 6 minterms set to . What is the number of maxterms in its POS canonical form?

Truth Table Hard
A. 10
B. 4
C. 6
D. 16

59 Which pair of expressions represents the same function, demonstrating SOP–POS duality?

SOP and POS Simplification Hard
A. and for 2 variables
B. and for 2 variables
C. and for 2 variables
D. and for 2 variables

60 A function is to be implemented. What is the minimum number of 2-input gates (any type) after full simplification?

Implementation of Boolean Functions Hard
A. needing 1 gate
B. needing 2 gates
C. needing 3 gates
D. needs 5 gates with no simplification
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