Explanation:

To implement the expression A + AB + ABC using NAND gates, we need to determine the minimum number of NAND gates required.

Basic understanding:

- A NAND gate is a universal gate, which means that any logic function can be implemented using only NAND gates.
- A NAND gate can be represented as a combination of an AND gate followed by a NOT gate.

Using De Morgan's theorem:

De Morgan's theorem states that any logic gate can be represented using only NAND gates by applying the following transformations:

1. NOT gate: A = NAND(A, A)
2. AND gate: A AND B = NAND(NAND(A, B), NAND(A, B))
3. OR gate: A OR B = NAND(NOT A, NOT B)

Implementing A:

To implement A, we can directly connect A to the input of a NAND gate. Therefore, no NAND gates are required.

Implementing AB:

To implement AB, we can use the NAND gate to perform the AND operation and then use another NAND gate to perform the NOT operation. The implementation steps are as follows:

1. Connect A and B to the inputs of a NAND gate (NAND1).
2. Connect the output of NAND1 to the input of another NAND gate (NAND2).
3. Connect the output of NAND2 to the output.

Implementing ABC:

To implement ABC, we can use the previously implemented AB and combine it with C using another NAND gate. The implementation steps are as follows:

1. Connect AB and C to the inputs of a NAND gate (NAND3).
2. Connect the output of NAND3 to the output.

Final implementation:

As we can see, the given expression A + AB + ABC can be implemented using only direct connections and a single NAND gate (NAND3) for the ABC term. Therefore, the minimum number of NAND gates required is 0.

Summary:

- The expression A + AB + ABC can be implemented using direct connections and a single NAND gate (NAND3) for the ABC term.
- No additional NAND gates are required for implementing A and AB.
- By applying De Morgan's theorem, any logic function can be implemented using only NAND gates.
- Therefore, the minimum number of NAND gates required is 0.