Boolean Expressions of Logic Gates

Introduction:
In digital electronics, logic gates are fundamental building blocks that perform logical operations on one or more binary inputs and produce a single binary output. These gates are represented by Boolean expressions, which describe the relationship between the inputs and the output.

Explanation:
The given options state various claims about the Boolean expressions of logic gates. Let's analyze each option to determine their correctness:

a) The boolean expression of an AND gate followed by an inverter is same as the boolean expression for a NAND gate:
- An AND gate produces a high output only when both of its inputs are high. The Boolean expression for an AND gate is given by:
Output = A * B, where A and B are the inputs.

- An inverter, also known as a NOT gate, produces the complement of its input. Therefore, the Boolean expression for an inverter is:
Output = NOT(A), where A is the input.

- When an AND gate is followed by an inverter, the resulting circuit is equivalent to a NAND gate. A NAND gate produces a low output only when both of its inputs are high. The Boolean expression for a NAND gate is:
Output = NOT(A * B), which is equivalent to NOT(A) + NOT(B).

- Therefore, the claim that the Boolean expression of an AND gate followed by an inverter is the same as the Boolean expression for a NAND gate is correct.

b) The boolean expression for an OR gate followed by a NOT gate is the same as that for a NOR gate:
- An OR gate produces a high output when one or both of its inputs are high. The Boolean expression for an OR gate is:
Output = A + B, where A and B are the inputs.

- Similar to the previous case, a NOT gate produces the complement of its input. The Boolean expression for a NOT gate is:
Output = NOT(A), where A is the input.

- When an OR gate is followed by a NOT gate, the resulting circuit is equivalent to a NOR gate. A NOR gate produces a low output only when both of its inputs are high. The Boolean expression for a NOR gate is:
Output = NOT(A + B), which is equivalent to NOT(A) * NOT(B).

- Therefore, the claim that the Boolean expression for an OR gate followed by a NOT gate is the same as the Boolean expression for a NOR gate is correct.

c) No two basic logic gates have the same boolean expression:
- This claim is incorrect. As demonstrated in the previous options, the Boolean expressions for specific combinations of logic gates can indeed be equivalent to other types of gates. The AND gate followed by an inverter is equivalent to a NAND gate, and the OR gate followed by a NOT gate is equivalent to a NOR gate.
- However, it is important to note that not all logic gates can be simplified or expressed in terms of each other. Each gate has its unique operation and truth table, which determines its Boolean expression.

Conclusion:
In summary, the correct options are a), b), and c). The Boolean expressions for specific combinations of logic gates can be equivalent to other types of gates, as demonstrated by the equivalence between an AND gate followed by an inverter and a NAND gate, as well