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

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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?
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.

1. AND Gate
2. OR Gate
3. NOT Gate.

Question 3.
Which basic gate is named as Inverter?
NOT Gate.

Question 4.
Which are the three logic operations?
AND, OR and NOT.

Question 5.
Write the standard symbol for AND Gate.

Question 6.
Write the truth table for AND Gate.

Question 7.
Write the logic circuit for AND Gate.

Question 8.
Write the standard symbol for OR gate.

Question 9.
Write the truth for OR Gate.

Question 10.
Write the logic circuit for OR Gate.

Question 11.
Write the standard symbol for NOT Gate.

Question 12.
Write the truth table for NOT Gate.

 I/P O/P X $$F=\bar{x}$$ 0 1 1 0

Question 13.
Write the Logic circuit for NOT Gate.

Question 14.
What is a truth table?
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?
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.
NAND and NOR.

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

Question 18.
What are the values of the two Input to a three input NAND gate, if its output is 1?

Question 19.
What are the values of the inputs to a three input NAND gate, if its o/p is 0?
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?
“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?
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?

Question 23.
For the truth table given below, what type of logic gate does the output x represent?

It represents NAND gate.

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

It represent X OR gate

Question 25.
State the principle duality of theorems in Boolean Algebra.
The Principle duality of theorem states that, “starting with a Boolean relation can be derived by

1. changing each OR sign (+) to an 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.
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.

Question 3.
Write the AND gate rule (write the output conditions).
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.

Question 5.
Write the OR gate rule (write the output conditions).
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.

 x $$F=\bar{x}$$ 0 1 1 0

truth table

Question 7.
Write the NOT gate rule, (write the output conditions).
NOT gate rule:

• 0 changing to 1
• 1 changing to 0

Question 8.
Write the truth table and standard symbol of NAND gate.

Question 9.
Explain the working of the NAND gate (write the o/p conditions).

• 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.

Question 11.
Explain the working of the NOR gate, (write the o/p conditions).

• 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)
AND operation:

OR Operation:

Question 13.
Draw the logic gate diagram to implement AND OR gate using NOR gate, (any two gates).
AND operations:

OR operation:

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

1. Only NOR gates
2. Only NAND gates.

1. only NOR gate.

2. only NAND gate

Question 15.
State De – Morgan’s theorems.
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.
The Principle duality of theorem states that, “starting with a Boolean relation can be derived by

1. changing each OR sign (+) to an AND sign (.)
2. changing each AND sign (.) to an OR sign (+)
3. 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)

1. o . x + xy + 1 . x
2. x(y + z) = xy + xz
3. $$x+\bar{x} y=x+y$$
4. 1 + x = l

1. o . x + xy + 1 . x → its dual → (1 + x) (x + y) (o + x)
2. x(y + z) = xy + xz → its dual → $$x(\bar{x}+y)$$ = (x+y) (x+z)
3. $$x+\bar{x} y$$ = x + y → its dual → $$x(\bar{x}+y)$$ = xy
4. 1 + x = 1 → its dual → 1 . x = 0

Question 18.
Simplify the following logical expressions using De – Morgan’s theorems,

1. (A + B) . C
2. (A + BC) (D + EF)

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.

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. $$x z+x \bar{y}+\overline{x}z$$

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,

1. $$x \bar{y} +x y=x$$
2. x + y = x + y

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,

1. $$Y=A B+\bar{B} C+\overline{C A}$$
2. $$\mathbf{Y}=\bar{\mathbf{x}} \bar{\mathbf{y}}+\mathbf{z} \overline{\mathbf{x}}+\bar{y}z$$

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.

1. $$\mathbf{A B} \bar {C}+\overline{\mathbf{A B C}}+\bar {\mathbf{A}} B\bar {\mathbf{C}}+\overline{\mathbf{A B}} C$$
2. $$\mathbf{A B}+\mathbf{A} \overline{\mathbf{B}}+\overline{\mathbf{A}} \mathbf{C}+\overline{\mathbf{A C}}$$

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,

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

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