Explanation:

To implement the given Boolean function A AB ABC using NAND gates, we need to first simplify the expression and then determine the minimum number of gates required.

Simplification:
Let's simplify the given expression step by step:

A AB ABC

= A AB (A BC) (Distributive property)

= A AB (A (B C)) (Associative property)

= A AB (A (B (B C))) (Idempotent property)

= A AB (A (B (B (A BC)))) (Associative property)

= A AB (A (B (B (A (B C))))) (Associative property)

Implementation:
Now, let's implement the simplified expression using NAND gates.

We can implement AND, OR, and NOT gates using NAND gates as follows:

- NAND gate as an AND gate:
- Connect the inputs of the NAND gate to the inputs of the AND gate.
- Connect the output of the NAND gate to the input of another NAND gate.

- NAND gate as an OR gate:
- Connect the inputs of the NAND gate to the inputs of the OR gate.
- Connect the output of the NAND gate to the input of another NAND gate.

- NAND gate as an NOT gate:
- Connect both inputs of the NAND gate together.
- Connect the output of the NAND gate to the input of another NAND gate.

Using the above conversions, we can implement the simplified expression using NAND gates as follows:

A AB ABC

= A AB (A (B (B (A (B C)))))

= NAND(NAND(A, B), NAND(NAND(A, NAND(B, C)), NAND(B, C)))

Minimum Number of Gates:
To find the minimum number of NAND gates required, we count the total number of NAND gates used in the implementation.

In the given expression, we have used:

- 7 NAND gates in total.

Therefore, the minimum number of NAND gates required to implement the Boolean function A AB ABC is 7 (option d).

Zero correct