SUMMARY: The chapter on Boolean Logic introduces the fundamental concepts of Boolean algebra and its application in computer science. KEY TOPICS: Boolean algebra, logic gates, truth tables, logical operators, De Morgan's laws, simplification of Boolean expressions, binary logic, applications of Boolean logic, digital circuits, logic circuit design
Which gate gives output 1 only when both inputs are 1?
AOR
BAND
CNOT
DNAND
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Correct answer: Option 2 — AND
Q21 Mark
The Boolean expression A + AB simplifies to:
AA
BB
CAB
DA + B
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Correct answer: Option 1 — A
Q31 Mark
The complement of a Boolean variable A is denoted as:
AA'
BA1
C!A
D~A
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Correct answer: Option 1 — A'
Q41 Mark
Which of the following is a universal gate?
AAND
BOR
CNOT
DNAND
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Correct answer: Option 4 — NAND
Q51 Mark
De Morgan's first theorem states that (A + B)' equals:
AA' + B'
BA' * B'
CA * B
DA + B
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Correct answer: Option 2 — A' * B'
Q61 Mark
What is the result of the Boolean expression A . (B + C)?
AA . B + A . C
BA + B . C
CA + B + C
DA . B . C
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Correct answer: Option 1 — A . B + A . C
Q71 Mark
Which of the following represents the AND operation in Boolean algebra?
A+
B*
C-
D/
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Correct answer: Option 2 — *
Q81 Mark
What is the output of the truth table for the expression A + A' ?
A0
B1
CA
DA'
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Correct answer: Option 2 — 1
Q91 Mark
Which of the following is NOT a logical operator in Boolean algebra?
AAND
BOR
CXOR
DNAND
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Correct answer: Option 4 — NAND
Q101 Mark
In a truth table, how many rows are there for a Boolean expression with three variables?
A4
B6
C8
D16
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Correct answer: Option 3 — 8
Q111 Mark
According to De Morgan's laws, which of the following is true?
A(A . B)' = A' + B'
B(A + B)' = A' + B'
C(A + B)' = A' . B'
D(A . B)' = A + B
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Correct answer: Option 1 — (A . B)' = A' + B'
Q121 Mark
What is the output of a NAND gate when both inputs are 0?
A0
B1
CUndefined
DDepends on the circuit
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Correct answer: Option 2 — 1
Q131 Mark
Which of the following Boolean expressions is equivalent to A + A . B?
AA + B
BA
CB
DA . B
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Correct answer: Option 2 — A
Q141 Mark
What is the primary purpose of using truth tables in Boolean logic?
ATo simplify expressions
BTo visualize circuit designs
CTo determine the output for all input combinations
DTo prove De Morgan's laws
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Correct answer: Option 3 — To determine the output for all input combinations
Q151 Mark
Which of the following circuits represents the logical expression A . (B + C)?
AAND gate followed by OR gate
BOR gate followed by AND gate
CTwo AND gates in series
DOne AND gate and one NOT gate
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Correct answer: Option 1 — AND gate followed by OR gate
Short Answer Questions10 questions
Q163 Marks
State and verify the two De Morgan's theorems.
Q173 Marks
Draw the truth tables for AND OR and NOT gates.
Q183 Marks
What is meant by a universal gate? Give one example.
Q193 Marks
Simplify the Boolean expression A.B + A.B' using identity laws.
Q203 Marks
Differentiate between NAND gate and NOR gate.
Q213 Marks
What is a truth table and how is it used in Boolean logic?
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A truth table is a mathematical table used to determine the output of a logical expression based on all possible combinations of its inputs. It systematically lists the input values and corresponding output values for each combination, helping in the analysis of logic gates and Boolean expressions.
Q223 Marks
Explain the concept of logical operators in Boolean algebra.
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Logical operators in Boolean algebra include AND, OR, and NOT. These operators are used to combine or modify Boolean values (true or false) to produce new Boolean values, forming the basis for constructing complex logical expressions and circuits.
Q233 Marks
What is the significance of binary logic in computer science?
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Binary logic is fundamental in computer science as it forms the basis of digital circuits and computing systems. It uses two states, typically represented as 0 and 1, to perform calculations and process information, enabling the operation of computers and electronic devices.
Q243 Marks
Describe the process of simplifying a Boolean expression using the consensus theorem.
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The consensus theorem states that AB + A'C + BC = AB + A'C. To simplify a Boolean expression using this theorem, identify terms that can be grouped according to the theorem and eliminate redundant terms, resulting in a more concise expression.
Q253 Marks
How do you derive the output of a logic circuit from a given Boolean expression?
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To derive the output of a logic circuit from a Boolean expression, first, identify the variables and operations involved. Then, construct the circuit using appropriate logic gates according to the expression, and finally evaluate the circuit for specific input values to determine the output.
Long Answer Questions6 questions
Q266 Marks
Explain the basic logic gates with their truth tables and symbols.
Q276 Marks
State and prove De Morgan's theorems with the help of truth tables.
Q286 Marks
Implement an XOR gate using only NAND gates with a circuit diagram.
Q296 Marks
Simplify the Boolean expression F = A.B + A.B' + A'.B using K-map and verify.
Q306 Marks
Discuss the importance of universal gates with implementation of basic gates using only NAND.
Q316 Marks
Compare AND OR and NOT logic gates with the help of a table giving truth table for each.
Assertion–Reason Questions8 questions
Q321 Mark
Assertion (A): NAND is called a universal gate.
Reason (R): Any logic gate can be constructed using only NAND gates.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q331 Mark
Assertion (A): A.A' is always 0.
Reason (R): A and its complement cannot be true at the same time.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q341 Mark
Assertion (A): An OR gate gives output 0 only when all inputs are 0.
Reason (R): Any one input being 1 gives output 1 in an OR gate.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q351 Mark
Assertion (A): Boolean algebra has only two values 0 and 1.
Reason (R): It is used to design digital circuits.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q361 Mark
Assertion (A): De Morgan's theorems are widely used in simplifying Boolean expressions.
Reason (R): They convert AND operations to OR operations and vice versa.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q371 Mark
Assertion (A): The output of an AND gate is 1 only when both inputs are 1.
Reason (R): An AND gate implements the logical conjunction operation.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q381 Mark
Assertion (A): The expression A + A' = 1 is a fundamental identity in Boolean algebra.
Reason (R): This identity states that a variable ORed with its complement equals true.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q391 Mark
Assertion (A): A NOR gate is a universal gate.
Reason (R): Universal gates can be used to create any other gate.
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Correct answer: Option 3 —
A is true, but R is false.
Statement-Based Questions8 questions
Q401 Mark
Statement 1: An XOR gate gives output 1 when inputs are different.
Statement 2: It gives output 0 when inputs are the same.
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Correct answer: Option 1 —
Both statements are true.
Q411 Mark
Statement 1: Boolean algebra was developed by George Boole in 1854.
Statement 2: It is the foundation of digital electronics.
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Correct answer: Option 1 —
Both statements are true.
Q421 Mark
Statement 1: A NOT gate has one input and one output.
Statement 2: It inverts the input.
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Correct answer: Option 1 —
Both statements are true.
Q431 Mark
Statement 1: A truth table lists all possible input combinations and outputs.
Statement 2: For n inputs there are 2^n rows in the truth table.
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Correct answer: Option 1 —
Both statements are true.
Q441 Mark
Statement 1: K-maps are used to simplify Boolean expressions.
Statement 2: They group adjacent 1s in powers of 2.
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Correct answer: Option 1 —
Both statements are true.
Q451 Mark
Statement 1: A NAND gate is a universal gate that can be used to create any other gate.
Statement 2: The output of an AND gate is true only when both inputs are false.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q461 Mark
Statement 1: De Morgan's laws state that the negation of a conjunction is the disjunction of the negations.
Statement 2: The output of an OR gate is true only when at least one input is true.
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Correct answer: Option 1 —
Both statements are true.
Q471 Mark
Statement 1: A NOR gate produces a true output only when both inputs are true.
Statement 2: Boolean expressions can be simplified using algebraic identities.
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Correct answer: Option 3 —
Only Statement 2 is true.
Case Study / Passage Questions4 questions
Q483 Marks
An engineer is designing a security circuit for an office. The alarm should ring (output Y = 1) only when both the door sensor (A) AND the motion sensor (B) detect intrusion. She decides to implement this with logic gates and considers using only NAND gates because they are universal.
Which gate gives output 1 only when both inputs are 1?
AAND
BOR
CNOT
DXOR
A NAND gate is called a:
AUniversal gate
BSpecialised gate
COutput gate
DCustom gate
Explain how an AND gate can be implemented using only NAND gates with a circuit diagram.
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1. Option 1 — AND
2. Option 1 — Universal gate
3. A NAND gate is universal because any other gate (AND OR NOT) can be built from NANDs. Y = A AND B is implemented by feeding A and B into a NAND then feeding that NAND output through another NAND with both inputs the same (which acts as a NOT). So 2 NANDs give an AND. Universal gates simplify manufacturing because the chip needs only one type of gate.
Q493 Marks
Boolean Logic is a branch of algebra that deals with true or false values, typically represented as 1 and 0. It forms the foundation of digital circuits and computer programming. The primary operations in Boolean algebra include AND, OR, and NOT, which can be combined to create complex logical expressions. Truth tables are used to represent the output of these operations based on all possible input combinations. For instance, the AND operation outputs true only when both inputs are true, while the OR operation outputs true if at least one input is true. Understanding these basic operations is crucial for designing efficient digital circuits and algorithms.
What are the primary operations in Boolean algebra?
AAND, OR, NOT
BAdd, Subtract, Multiply
CXOR, NAND, NOR
DIncrement, Decrement, Shift
Explain the significance of truth tables in Boolean logic.
Which Boolean operation outputs true only when both inputs are true?
AAND
BOR
CNOT
DXOR
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1. Option 1 — AND, OR, NOT
2. Truth tables are used to represent the output of Boolean operations based on all possible input combinations, helping to visualize and analyze logical expressions.
3. Option 1 — AND
Q503 Marks
De Morgan's laws are fundamental rules in Boolean algebra that describe how the NOT operator interacts with AND and OR operators. The first law states that the negation of a conjunction is equivalent to the disjunction of the negations, which can be expressed as NOT (A AND B) = (NOT A) OR (NOT B). The second law states that the negation of a disjunction is equivalent to the conjunction of the negations, expressed as NOT (A OR B) = (NOT A) AND (NOT B). These laws are essential for simplifying complex Boolean expressions and are widely used in digital circuit design.
What does the first of De Morgan's laws state?
ANOT (A AND B) = (NOT A) OR (NOT B)
BNOT (A OR B) = (NOT A) AND (NOT B)
CA AND B = NOT (A OR B)
DA OR B = NOT (A AND B)
How do De Morgan's laws assist in Boolean expression simplification?
What is the second of De Morgan's laws?
ANOT (A OR B) = (NOT A) AND (NOT B)
BNOT (A AND B) = (NOT A) OR (NOT B)
CA AND B = NOT (A OR B)
DA OR B = NOT (A AND B)
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1. Option 1 — NOT (A AND B) = (NOT A) OR (NOT B)
2. De Morgan's laws provide a systematic way to transform and simplify complex Boolean expressions, making it easier to design and analyze digital circuits.
3. Option 1 — NOT (A OR B) = (NOT A) AND (NOT B)
Q513 Marks
In digital circuits, logic gates are the building blocks that perform basic logical functions. The most common types of logic gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each gate has a specific function and can be combined to create complex circuits. For example, an AND gate outputs true only when all its inputs are true, while an OR gate outputs true if at least one input is true. Understanding how these gates work and how to represent them in truth tables is crucial for designing effective digital systems.
Which logic gate outputs true only when all its inputs are true?
AAND gate
BOR gate
CNOT gate
DXOR gate
What is the role of logic gates in digital circuits?
Name one type of logic gate that outputs true if at least one input is true.
AOR gate
BAND gate
CNOT gate
DNAND gate
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1. Option 1 — AND gate
2. Logic gates perform basic logical functions and are combined to create complex circuits, enabling the processing of binary information.
3. Option 1 — OR gate
Table-Based Questions4 questions
Q525 Marks
Identify the gate from the truth table (A, B inputs and Y output).
A
B
Gate 1 (Y=AB)
Gate 2 (Y=A+B)
Gate 3 (Y=AB')
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
Q535 Marks
For each Boolean expression, give the simplified form using identity laws.
Expression
Simplified
A + 0
?
A + 1
?
A . 0
?
A + A
?
A + A'
?
A . A'
?
Q543 Marks
Study the truth table for three logic gates and answer:
A
B
AND (A.B)
OR (A+B)
XOR (A^B)
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
Which gate gives output 1 only when inputs are different?
AAND
BOR
CXOR
DNOT
An OR gate gives output 0 only when:
ABoth 0
BBoth 1
CDifferent
DCannot tell
Construct the truth tables of NAND NOR and XNOR gates from this table.
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1. Option 3 — XOR
2. Option 1 — Both 0
3. The truth table lists all 4 input combinations of two inputs A and B. AND gives 1 only when both inputs are 1. OR gives 1 if any input is 1. XOR (exclusive OR) gives 1 only when inputs differ. NAND NOR XNOR are inverses of AND OR XOR respectively. Truth tables completely specify gate behaviour.
Q556 Marks
What is the output of the AND gate when both inputs are true?
Input A
Input B
Output (A AND B)
True
True
True
False
False
True
False
False
Picture-Based Questions1 question
Q563 Marks
Study the truth tables of AND OR XOR gates and answer:
Which gate gives output 1 only when both inputs are 1?
AAND
BOR
CXOR
DNOT
Which gate gives output 1 only when inputs are different?
AAND
BOR
CXOR
DNAND
Construct truth tables for NAND NOR and XNOR from these.
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1. Option 1 — AND
2. Option 3 — XOR
3. The truth table lists all 4 input combinations of two inputs. AND gives 1 only when both inputs are 1. OR gives 1 if any input is 1. XOR gives 1 only when inputs differ. NAND NOR XNOR are inverses of AND OR XOR. Truth tables completely specify gate behaviour.
