The problem provides a logic circuit diagram composed of logic gates with inputs A and B, and output F. The questions ask to: i. Identify the logic gates used in the circuit. ii. Derive the Boolean expression for the output F in terms of inputs A and B. iii. Construct the truth table for the Boolean expression. iv. Determine the basic logic gate represented by the circuit.

1. Problem Description

The problem provides a logic circuit diagram composed of logic gates with inputs A and B, and output F. The questions ask to:

i. Identify the logic gates used in the circuit.

ii. Derive the Boolean expression for the output F in terms of inputs A and B.

iii. Construct the truth table for the Boolean expression.

iv. Determine the basic logic gate represented by the circuit.

2. Solution Steps

i. The two logic gates present in the circuit diagram are the NOT gate (inverters) and the NAND gate.

ii. To find the Boolean expression, let's analyze the circuit:

- The input A is inverted to $\bar{A}$.

- The input B is inverted to $\bar{B}$.

- The inverted inputs $\bar{A}$ and $\bar{B}$ are fed into a NAND gate.

- The output of a NAND gate is the negation of the AND of its inputs.

- Therefore, $F = \overline{\bar{A} \cdot \bar{B}}$.

- Using DeMorgan's Law, $\overline{X \cdot Y} = \overline{X} + \overline{Y}$, we have $F = \overline{\bar{A}} + \overline{\bar{B}} = A + B$.

- So, $F = A + B$.

iii. The truth table for $F = A + B$ (OR gate) is:

| A | B | F |

|---|---|---|

| 0 | 0 | 0 |

| 0 | 1 | 1 |

| 1 | 0 | 1 |

| 1 | 1 | 1 |

iv. The basic logic gate represented by the circuit is an OR gate.

3. Final Answer

i. NOT gate and NAND gate.

ii. $F = A + B$

iii. Truth Table:

| A | B | F |

|---|---|---|

| 0 | 0 | 0 |

| 0 | 1 | 1 |

| 1 | 0 | 1 |

| 1 | 1 | 1 |

iv. OR gate.