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## 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:

A Gate is an electronic circuit which operates on one or more signals and always produces an output signal.

Question 2.

Mention the 3 basic Logic Gates.

Answer:

- AND Gate
- OR Gate
- NOT Gate.

Question 3.

Which basic gate is named as Inverter?

Answer:

NOT Gate.

Question 4.

Which are the three logic operations?

Answer:

AND, OR and NOT.

Question 5.

Write the standard symbol for AND Gate.

Answer:

Question 6.

Write the truth table for AND Gate.

Answer:

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 for OR Gate.

Answer:

Question 10.

Write the logic circuit for OR Gate.

Answer:

Question 11.

Write the standard symbol for NOT Gate.

Answer:

Question 12.

Write the truth table for NOT Gate.

Answer:

I/P | O/P |

X | \( F=\bar{x} \) |

0 | 1 |

1 | 0 |

Question 13.

Write the Logic circuit for NOT Gate.

Answer:

Question 14.

What is a truth table?

Answer:

Truth table table which represent all the possible values of Logical variables / statements along with all the possible result for the given combinations of values.

Question 15.

What is meant by universal Gates?

Answer:

Universal gate is a gate.:using which all the basic gates can be designed. NAND and NOR are called as universal Gates.

Question 16.

Mention different universal Gates.

Answer:

NAND and NOR.

Question 17.

What is the output of the two Input NAND gate for the inputs : A = 0, B = 1?

Answer:

1.

Question 18.

What are the values of the two Input 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 o/p is 0?

Answer:

All are 1

x | y | z | \( F=\overline{x y z} \) |

1 | 1 | 1 | 0 |

Question 20.

What is the output of the two input OR Gate for the inputs A = 0, B = 0?

Answer:

“0”

x | y | F = x + y |

0 | 0 | 0 |

Question 21.

What are the values of the inputs to a 3 input OR Gate if its output is 0?

Answer:

All are 1

x | y | z | F = x + y + x |

0 | 0 | 0 | 0 |

Question 22.

What are the values of the inputs to a three input OR gate if its output is 1?

Answer:

Question 23.

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

Answer:

It represents NAND gate.

Question 24.

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

Answer:

It represent X OR gate

Question 25.

State the principle duality of theorems in Boolean Algebra.

Answer:

The Principle duality of theorem states that, “starting with a Boolean relation can be derived by

- changing each OR sign (+) to an 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:

Boolean theorems can be proved by substituting all possible values of the variables that are 0 and 1. This technique of proving theorems is called proof by perfect induction.

Proof:

1. 0 + x = x

If x = 0, then LHS = 0 + 0

= 0

= x

= RHS.

If x = 1, then LHD = 0 + 1

= 1

= x

= RHS.

Thus for every value of x, 0 + x =x always.

2. 1 + x = 1

If x = 0, then LHS = 1 + 0

= 1

= RHS

If x = 1, then LHS = 1 + 1

= 1

= RHS.

Thus, for every value of x, 1 + x = 1 always.

3. 0 . x = 0

If x = 0, then LHS = 0 . 0

= 0

= RHS

If x = 1, then LHS = 0 . 1

= 0

= RHS.

Thus for every value of x, o . x = 0 always.

Question 2.

Write the truth tables and standard symbols of AND Gate.

Answer:

Question 3.

Write the AND gate rule (write the output conditions).

Answer:

AND gate rule:

- 0 . 0 = 0
- 0 . 1 = 0
- 1 . 0 = 0
- 1 . 1 = 1

Question 4.

Write the truth tables and standard symbol of OR gate.

Answer:

Question 5.

Write the OR gate rule (write the output conditions).

Answer:

OR gate rule:

- 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:

x | \( F=\bar{x} \) |

0 | 1 |

1 | 0 |

truth table

Question 7.

Write the NOT gate rule, (write the output conditions).

Answer:

NOT gate rule:

- 0 changing to 1
- 1 changing to 0

Question 8.

Write the truth table and standard symbol of NAND gate.

Answer:

Question 9.

Explain the working of the NAND gate (write the o/p conditions).

Answer:

- 0 . 0 = 0 → 1 If both the input are high, the
- 0 . 1 = 0 → 1 output is low, for remaining
- 1 . 0 = 0 → 1 inputs output is high.
- 1 . 1 = 1 → 0

Question 10.

Write the truth table and standard symbol of NOR gate.

Answer:

Question 11.

Explain the working of the NOR gate, (write the o/p conditions).

Answer:

- 0 + 0 = 0 → 1 If both the inputs are low
- 0 + 1 = 1 → 1 output is low and for
- 1 + 0 = 1 → 0 remaining inputs output is high.
- 1 + 1 = 1 → 0

OR

If any one I/P is high o/p is high.

Question 12.

Draw the logic gate diagram to implement AND and OR gate using NAND gates. (Any two gates)

Answer:

AND operation:

OR Operation:

Question 13.

Draw the logic gate diagram to implement AND OR gate using NOR gate, (any two gates).

Answer:

AND operations:

OR operation:

Question 14.

Draw the logic gates diagram to implement NOT gate using

- Only NOR gates
- Only NAND gates.

Answer:

1. only NOR gate.

2. only NAND gate

Question 15.

State De – Morgan’s theorems.

Answer:

De-morgan’s first Theorem

\(\overline{x+y}=\bar{x} \cdot \bar{y}\)

Statement De-morgan’s 1st theorem states that ” sum of the complement of any 2 variables is equal to the product of complements of variables”.

Proof:

LHS = RHS. Hence proved.

De- morgan’s second Theorem:

\(\overline{x \cdot y}=\bar{x}+\bar{y}\)

Statement Demorgan’s 2nd Theorem states that ” Product of complement of variables is equal to the sum of the complement of variables”.

Proof:

LHS = RHS. Hence proved.

Question 16.

What is principle of duality? Given an example.

Answer:

The Principle duality of theorem states that, “starting with a Boolean relation can be derived by

- changing each OR sign (+) to an AND sign (.)
- changing each AND sign (.) to an OR sign (+)
- changing each 0 by 1 and each 1 by 0.

Ex: X + 1 = 0 dual X . 0 = 0

Question 17.

Give the dual form of (any two)

- o . x + xy + 1 . x
- x(y + z) = xy + xz
- \(x+\bar{x} y=x+y\)
- 1 + x = l

Answer:

- o . x + xy + 1 . x → its dual → (1 + x) (x + y) (o + x)
- x(y + z) = xy + xz → its dual → \(x(\bar{x}+y)\) = (x+y) (x+z)
- \(x+\bar{x} y\) = x + y → its dual → \(x(\bar{x}+y)\) = xy
- 1 + x = 1 → its dual → 1 . x = 0

Question 18.

Simplify the following logical expressions using De – Morgan’s theorems,

- (A + B) . C
- (A + BC) (D + EF)

Answer:

1. (A + B) . C

According to De- Morgan’s law \(\overline{x . y}=\bar{x}+\bar{y}\)

\(\overline{(A+B) \cdot C}=\overline{(A+B)}+\bar{C}\)

= \((\overline{\mathrm{A}} \cdot \overline{\mathrm{B}})+\overline{\mathrm{C}}\)

2. (A + BC) (D + EF)

According to De-Morgan’s law \(\overline{x . y}=\bar{x}+\bar{y}\)

Question 19.

Prepare a truth of combinations for the following Boolean algebra expressions.

- \(\mathbf{A} \overline{\mathbf{B}} \overline{\mathbf{C}}+\overline{\mathbf{A}} \mathbf{B}\)
- \(\overline{\mathbf{A B C}}+\mathbf{A C}+\mathbf{A B}\)
- \(x z+x \bar{y}+\overline{x}z\)

Answer:

1. \(\mathbf{A} \overline{\mathbf{B}} \overline{\mathbf{C}}+\overline{\mathbf{A}} \mathbf{B}\)

2. \(\overline{\mathbf{A B C}}+\mathbf{A C}+\mathbf{A B}\)

3. \(x z+x \bar{y}+\overline{x}z\)

Question 20.

Prove the following rules using the proof by perfect induction,

- \(x \bar{y} +x y=x\)
- x + y = x + y

Answer:

1. \(x \bar{y} +x y=x\)

Hence proved.

2. x + y = x + y

If x = 0, LHS = 0 + y = y

RHS = 0 + y = y

LHS = RHS.

If x = 1, LHS = 1 + y = 1

RHS = 1 +y = 1

∴ LHS = RHS.

x + y = x +y

Hence proved.

Question 21.

Draw logic circuit diagram for the following expressions,

- \(Y=A B+\bar{B} C+\overline{C A}\)
- \(\mathbf{Y}=\bar{\mathbf{x}} \bar{\mathbf{y}}+\mathbf{z} \overline{\mathbf{x}}+\bar{y}z\)

Answer:

1. \(Y=A B+\bar{B} C+\overline{C A}\)

2. \(\mathbf{Y}=\bar{\mathbf{x}} \bar{\mathbf{y}}+\mathbf{z} \overline{\mathbf{x}}+\bar{y}z\)

Question 22.

Simplify the following Boolean expressions.

- \(\mathbf{A B} \bar {C}+\overline{\mathbf{A B C}}+\bar {\mathbf{A}} B\bar {\mathbf{C}}+\overline{\mathbf{A B}} C\)
- \(\mathbf{A B}+\mathbf{A} \overline{\mathbf{B}}+\overline{\mathbf{A}} \mathbf{C}+\overline{\mathbf{A C}}\)

Answer:

1. \(\mathbf{A B} \bar {C}+\overline{\mathbf{A B C}}+\bar {\mathbf{A}} B\bar {\mathbf{C}}+\overline{\mathbf{A B}} C\)

2. \(\mathbf{A B}+\mathbf{A} \overline{\mathbf{B}}+\overline{\mathbf{A}} \mathbf{C}+\overline{\mathbf{A C}}\)

Question 23.

Complement the following expressionas & simplify,

- \(\overline{x y}+x \bar{y}\)
- \(x \bar{y} z+\bar{x} \bar{y}\)
- \(\overline{\mathbf{x}}(y+\overline{\mathbf{z}})\)
- \(x(y \bar{z}+\bar{y} z)\)

Answer:

1. \(\overline{x y}+x \bar{y}\)

2. \(x \bar{y} z+\bar{x} \bar{y}\)

3. \(\overline{\mathbf{x}}(y+\overline{\mathbf{z}})\)

4. \(x(y \bar{z}+\bar{y} z)\)