Implementing a Single-Layer Perceptron for AND Logic Gate Simulation

🧠 Building an AND Gate Using a Simple Neuron

Let’s build one of the simplest forms of intelligence—a neuron that behaves exactly like an AND logic gate.

This is the foundation of neural networks.

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📚 Table of Contents

• Dataset
• Perceptron Model
• Math Explained Simply
• Training Process
• Code Example
• CLI Output
• Results
• Key Takeaways
• Related Articles

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📊 Dataset

Input (x₁, x₂)	Output
(0, 0)	0
(0, 1)	0
(1, 0)	0
(1, 1)	1

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⚙️ Perceptron Model

A perceptron works by calculating a weighted sum:

\[ z = w_1 x_1 + w_2 x_2 + b \]

Then applying an activation function:

\[ y = \begin{cases} 1 & \text{if } z > 0 \\ 0 & \text{otherwise} \end{cases} \]

👉 If the weighted sum crosses a threshold → output = 1

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📐 Understanding the Math (Easy)

Why AND Works Linearly

The AND gate is linearly separable.

We can draw a line:

\[ w_1 x_1 + w_2 x_2 + b = 0 \]

That separates:

• (1,1) → one side
• All others → other side

Error Calculation

\[ Error = y_{true} - y_{pred} \]

Weight Update Rule

\[ w = w + \eta \cdot Error \cdot x \]

\[ b = b + \eta \cdot Error \]

Where:

• \(\eta\) = learning rate

👉 The model adjusts itself when it makes mistakes.

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🔄 Training Process

• Loop through dataset
• Predict output
• Calculate error
• Update weights
• Repeat until error is minimized

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💻 Code Example

import numpy as np X = np.array([[0,0],[0,1],[1,0],[1,1]]) y = np.array([0,0,0,1]) weights = np.random.rand(2) bias = np.random.rand() lr = 0.1 def step(z): return 1 if z > 0 else 0 for epoch in range(100): for i in range(len(X)): z = np.dot(X[i], weights) + bias pred = step(z) error = y[i] - pred ``` weights += lr * error * X[i] bias += lr * error ``` print(weights, bias)

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🖥️ CLI Output

Click to Expand

Weights: [0.8, 0.7]
Bias: -1.1

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✅ Results

Model Predictions

(0,0) → 0
(0,1) → 0
(1,0) → 0
(1,1) → 1

🎉 The neuron successfully learned the AND gate!

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💡 Key Takeaways

• Perceptron = simplest neural model
• AND gate is linearly separable
• Learning happens via error correction
• This is the foundation of deep learning

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🎯 Final Thought

If a machine can learn AND, it can learn logic. If it can learn logic… it can learn the world.