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.

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:

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:

Question 8.

Write the standard symbol for OR gate.

Answer:

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 |

Question 10.

Write the logic circuit for OR gate.

Answer:

Question 11.

Write the standards symbol for NOT gate.

Answer:

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:

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.

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:

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:

Question 23.

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

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.

- Changing each OR sign (+) to and AND sign (.)
- Changing each AND sign (.) to an OR sign (+)
- 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

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 |

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.

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.

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

The standard symbol of NAND gate.

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.

Question 10.

Write the truth table and standard symbol of NOR gate.

Answer:

The truth table of NOR gate

The standard symbol of NOR gate

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.

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

Implementing OR using NAND gates

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

Implementing OR using NOR gates

Question 14.

Draw the logic gate diagram to implement NOT using

- Only NOR gates
- Only NAND gates.

Answer:

The logic gate diagram to implement NOT using only NOR gates

The logic gate diagram to implement NOT using only NAND gates

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

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

For example, (X + Y’) dual is (X’. Y)

Question 17.

Give the dual form of (any two)

- 0.X + X.Y + 1.X
- X.(Y+Z) = X.Y + X.Z
- X + X’.Y = X + Y
- 1 + X = 1

Answer:

The dual form of

- 0.X + X.Y + 1.X is 1 + X’. X’ + Y’. 0 + X’
- X.(Y+Z) = X.Y + X.Z is X’ + (Y’.Z’) = X’ + Y’. X’ + Z’
- X + X’.Y = X + Y is X’. X + Y’ = X’. Y’
- 1 + X = 1 is 0.X = X.

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

2. A’B’C’ + AC + AB

3. XZ + XY’ + X’Z

Question 20.

Prove the following rules using the proof by perfect induction.

- XY’ + XY = X
- 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)’

2. Y = (XY)’ + ZX’ + Y’Z

Question 22.

Simplify the following Boolean expressions.

Answer:

Question 23.

Complement the following expressions and simplify.

Answer: