🔐 Understanding and Implementing an N-Input AND Gate in C++

🧠 What is an AND Gate?

In digital logic, an AND gate is a basic logic gate that outputs:

• 1 (True) only if all of its inputs are 1

• 0 (False) if even one input is 0

🔧 Truth Table for 2-input AND Gate:

For more than two inputs, the same principle applies — all must be 1 for the result to be 1.

🧩 Problem Statement

💬 Question:

Construct an N-input AND Gate in C++.
Input: First line has an integer N. Second line has N binary integers (0 or 1).
Output: 1 if all inputs are 1, otherwise 0.

🧾 Example:

Input:

4  
1 1 1 0

Output: 0

Why? Because one of the inputs is 0, and the AND gate fails if any input is 0.

🧮 Real-World Analogy

Imagine a team project where every member must submit their part.
If even one person fails to submit, the project fails.
That’s exactly how an AND gate behaves — all must be 1 (submitted) to succeed.

🧑‍💻 Approach

1. Read the number of inputs N.

2. Initialize a variable result = 1 (we assume all are 1 to begin with).

3. Loop through all inputs and update result using bitwise AND:

    result = result & input;
   

4. If any input is 0, result will become 0.

5. Finally, print the result.

💻 C++ Code

Output

🔍 Why Bitwise AND Works Here

The bitwise AND (&) compares two bits and returns:

• 1 if both are 1

• 0 otherwise

So when we keep doing result = result & input, if even one input is 0, the whole result becomes 0.

This is faster and cleaner than using if conditions.

🧮 Dry Run Example

Input:

n = 4  
values = 1 1 1 0

✅ Final Output: 0
Reason: One of the inputs is 0 → AND gate outputs 0

---

🧠 Bitwise AND (&) Logic

• 1 & 1 = 1

• 1 & 0 = 0

• 0 & 0 = 0

The AND gate fails if even one input is 0, which is exactly how & behaves in C++.

⏱️ Time & Space Complexity

• Time Complexity: O(N)

• Space Complexity: O(1)

🧪 Sample Test Cases

✅ Test 1:

Input:

3  
1 1 1

Output: 1

---

❌ Test 2:

Input:

5  
1 1 0 1 1

Output: 0

---

⚠️ Edge Case:

Input:

1  
0

Output: 0

---

📌 Conclusion

Simulating an AND gate in C++ is a great way to understand both:

• Basic bitwise operations

• Logic simulation techniques used in hardware/software design

It’s also a common beginner-level coding problem asked in interviews and technical rounds.