2nd PUC Computer Science Question Bank Chapter 3 Logic Gates

   

You can Download Chapter 3 Logic Gates Questions and Answers, Notes, 2nd PUC Computer Science Question Bank with Answers Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Computer Science Question Bank Chapter 3 Logic Gates

2nd PUC Computer Science Logic Gates One Mark Questions and Answers

Question 1.
What is a logic gate?
Answer:
It is an electronic circuit having one or more than one input and only one output.

Question 2.
Mention the three basic logic gates.
Answer:
The three basic logic gates are NOT, OR and AND gate.

KSEEB Solutions

Question 3.
Which basic gate is named as Inverter?
Answer:
The NOT gate is named as Inverter.

Question 4.
Which are the three logic operations?
Answer:
The three logic operations are Nor, Or and And.

Question 5.
Write the standard symbol for AND gate.
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 1

Question 6.
Write the truth table for AND gate.
Answer:

A B Y = A.B
0 0 0
0 1 0
1 0 0
1 1 1

Question 7.
Write the logic circuit for AND gate.
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 2

Question 8.
Write the standard symbol for OR gate.
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 3

Question 9.
Write the truth table for OR gate.
Answer:

A B  Y = A+B
0 0 0
0 1 1
1 0 1
1 1 1

KSEEB Solutions

Question 10.
Write the logic circuit for OR gate.
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 4

Question 11.
Write the standards symbol for NOT gate.
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 5

Question 12.
Write the truth table for NOT gate.
Answer:

A Y = A’
0 1
1 0

Question 13.
Write the logic circuit for NOT gate.
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 6

Question 14.
What is a truth table?
Answer:
A table that represents all possible values of logical variables along with all the possible results of the given combinations of values.

Question 15.
What is meant by universal gates?
Answer:
A gate which can be used to create any Logic gate is called Universal Gate.

Question 16.
Mention different universal gates.
Answer:
The different universal gates are NAND and NOR.

KSEEB Solutions

Question 17.
What is the output of the two-input NAND gate for the inputs: A=0, B=1?
Answer:
The output of the two-input NAND gate for the input A=0, B=1 is 1.

Question 18.
What are the values of the inputs to a three-input NAND gate, if its output is 1?
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 7

Question 19.
What are the values of the inputs to a three-input NAND gate, if its output is 0?
Answer:

X Y z (XYZ)’
1 1 1 0

Question 20.
What is the output of the two-input OR gate for the inputs: A=0, B=0?
Answer:
The output of the two-input OR gate for the inputs A=0, B=0 is 0.

Question 21.
What are the values of the inputs to a three-input OR gate, if its output is 0?
Answer:

X Y z Y=X+Y+Z
0 0 0 0

Question 22.
What are the values of the inputs to a three-input OR gate, if the output is 1?
Answer:
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 8

Question 23.
For the truth table given below, what type of logic gate does the output X represent?
2nd PUC Computer Science Logic Gates One Mark Questions and Answers 9
Answer:
The type of logic gate that the output X represent is NAND.

Question 24.
For the truth table given below, what type of logic gate does the output X represent?

A B X
0 0 0
0 1 1
1 0 1
1 1 0

Answer:
The logic gate XOR generates the output mentioned in the above truth table.

Question 25.
State the principle duality of theorems in Boolean algebra.
Answer:
The principle of duality theorems states that starting with a Boolean relation another Boolean relation can be derived by.

  1. Changing each OR sign (+) to and AND sign (.)
  2. Changing each AND sign (.) to an OR sign (+)
  3. Changing each 0 by 1 and each 1 by 0.

2nd PUC Computer Science Logic Gates Three Marks Questions and Answers

Question 1.
What is meant by proof by perfect induction? Give an example.
Answer:
It is a method of proving Boolean theorems by substituting all possible values of the variables. The possible values of the variables are 0 and 1.
For example, 0 + X = X
If X = 0, then LHS = 0 + X
= 0 + 0
= 0
If X = 1, then LHS = 0 + X
= 0 + 1
= 1

Question 2.
Write the truth table and standard symbol of AND gate.
Answer:
The standard symbol of AND gate is
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 10
The truth table of AND (Y=A.B)

A B Y = A.B
0 0 0
0 1 0
1 0 0
1 1 1

KSEEB Solutions

Question 3.
Write the AND gate rule. (Write the output conditions)
Answer:
The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high.

A B Y=A.B
0 0 0
0 1 0
1 0 0
1 1 1

Question 4.
Write the truth table and the standard symbol of the OR gate.
Answer:
The standard symbol of the OR gate.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 11
The truth table for the OR gate.

A B Y=A+B
0 0 0
0 1 1
1 0 1
1 1 1

Question 5.
Write the OR gate rule, (write the output conditions)
Answer:
The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high.

A B Y=A+B
0 0 0
0 1 1
1 0 1
1 1 1

Question 6.
Write the truth table and standard symbol of NOT gate.
Answer:
The truth table of NOT

A Y=A’
0 1
1 0

The standard symbol of NOT gate.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 12

Question 7.
Write the NOT gate rule, (write the output conditions)
Answer:
The NOT gate is an electronic circuit that produces an inverted version of the input as its output. It is also known as an inverter.

A Y=A’
0 1
1 0

Question 8.
Write the truth table and standard symbol of NAND gate.
Answer:
The truth table of NAND gate
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 13
The standard symbol of NAND gate.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 14

Question 9.
Explain the working of NAND gate, (write the output conditions)
Answer:
This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate. The outputs of all NAND gates are high if any of the inputs are low.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 15

Question 10.
Write the truth table and standard symbol of NOR gate.
Answer:
The truth table of NOR gate
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 16
The standard symbol of NOR gate
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 17

Question 11.
Explain the working of NOR gate, (write the output conditions)
Answer:
This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate. The outputs of all NOR gates are low if any of the inputs are high.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 18

Question 12.
Draw the logic gate diagram to implement AND and OR gates using NAND gates only, (any two gates)
Answer:
Implementing AND using NAND gates
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 19
Implementing OR using NAND gates
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 20

KSEEB Solutions

Question 13.
Draw the logic gate diagram to implement AND and OR gates using NOR gates only. (Any two gates).
Answer:
Implementing AND using NOR gates
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 21
Implementing OR using NOR gates
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 22

Question 14.
Draw the logic gate diagram to implement NOT using

  1. Only NOR gates
  2. Only NAND gates.

Answer:
The logic gate diagram to implement NOT using only NOR gates
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 23
The logic gate diagram to implement NOT using only NAND gates
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 24

Question 15.
State De Morgan’s theorems.
Answer:
1. De Morgan’s theorem 1:
When the OR sum of two variables is inverted, this is the same as. inverting each variable individually and then ANDing these inverted variables.
(X + Y)’ = X’. Y’

2. De Morgan’s theorem 2:
When the AND product of two variables is inverted, this is the same as inverting each variable individually and then ORing them.
(X.Y)’ = X’ + Y’

Question 16.
What is the principle of duality? Give an example.
Answer:
The principle of duality states that starting with a Boolean relation, another relation can be derived by

  1. Changing each OR sing (+) to an AND sign (.)
  2. Changing each AND sing (.) to an OR sign (+).
  3. Replacing each 0 by 1 and each 1 by 0.
  4. All variables are complemented.

For example, (X + Y’) dual is (X’. Y)

Question 17.
Give the dual form of (any two)

  1. 0.X + X.Y + 1.X
  2. X.(Y+Z) = X.Y + X.Z
  3. X + X’.Y = X + Y
  4. 1 + X = 1

Answer:
The dual form of

  1. 0.X + X.Y + 1.X   is 1 + X’. X’ + Y’. 0 + X’
  2. X.(Y+Z) = X.Y + X.Z  is  X’ + (Y’.Z’) = X’ + Y’. X’ + Z’
  3. X + X’.Y = X + Y  is  X’. X + Y’ = X’. Y’
  4. 1 + X = 1  is  0.X = X.

KSEEB Solutions

Question 18.
Simplify the following logical expression using De Morgan’s theorems.
Answer:
1. (A + B).C
= AC + BC.

2. (A + BC). (D + EF)
(A + BC) . D + (A + BC). EF
AD + BCD + AEF + BCEF.

Question 19.
Prepare the truth of combinations for the following Boolean algebra expressions.
Answer:
1. AB’C’ + A’B
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 25

2. A’B’C’ + AC + AB
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 26

3. XZ + XY’ + X’Z
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 27

Question 20.
Prove the following rules using the proof by perfect induction.

  1. XY’ + XY = X
  2. X+Y=Y+X

Answer:
1. XY’ + XY = X
By proof of perfect induction X = 0, Y =1
XY’ + XY = X
LHS = 0.0 + 0.1 = 0 + 0 = 0
By proof of perfect induction X = 1, Y = 0
LHS = 1.1 + 1.0 = 1 + 0 = 1.

2. X + Y = Y + X
By proof of perfect induction X = 0, Y = 1
LHS = 0 + 1 = 1
RHS = 1 + 0=1
LHS = RHS
By proof of perfect induction X = 1, Y = 0
LHS = 1 + 0 = 1
RHS = 0 + 1 = 1
LHS = RHS

Question 21.
Draw logic circuit diagram for the following expressions.
Answer:
1. Y = AB + B’C + (CA)’
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 28
2. Y = (XY)’ + ZX’ + Y’Z
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 29

Question 22.
Simplify the following Boolean expressions.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 30
Answer:
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 31

Question 23.
Complement the following expressions and simplify.
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 32
Answer:
2nd PUC Computer Science Logic Gates Three Marks Questions and Answers 33

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