Implementation of Perceptron Algorithm for NAND Logic Gate with 2-bit Binary Input

A Perceptron is one of the simplest types of deep learning models. It is used to make decisions based on input values and is like a basic brain cell that can "learn" to give output like 0 or 1 from given inputs. In this article, we will show how a perceptron can be used to perform the task of NAND logic gate. A NAND gate gives output of 0 only when both inputs are 1. In all other cases the output is 1. NAND Truth Table is:

It is the opposite of the AND gate that's why it is called NAND gate (Not of And gate).

Perceptron for NAND Gate

A perceptron takes binary inputs, multiplies them with weights, adds a bias and passes the result through an activation function usually a step function.

y = \Theta(w_1 x_1 + w_2 x_2 + b)

where:

• x_1, x_2: Inputs
• w_1, w_2:​Weights for the inputs
• b: Bias
• \Theta(z): Step function

Step Function:

\Theta(z) = \begin{cases}1 & \text{if } z \geq 0 \\0 & \text{if } z < 0\end{cases}

Choose Weights and Bias for NAND

We need to find w_1, w_2,and, b such that the perceptron behaves like a NAND gate. Let’s use this configuration:

• w_1 = -1
• w_2 = -1
• b = 1.5

The inputs x_1 \,and\,x_2go into the perceptron. The weights and bias are used to calculate the weighted sum. and the step function determines the output.

Let’s implement this into Python.

Step 1: Define the Step Activation Function

import numpy as np

def step_function(z):
    return 1 if z >= 0 else 0

Step 2: Perceptron logic for 2 inputs

def perceptron(x1, x2, w1, w2, b):
    z = (x1 * w1) + (x2 * w2) + b
    return step_function(z)

Step 3: Set weights and bias

w1 = -1
w2 = -1
b = 1.5

Step 4: Test all combinations

print("NAND Gate Output:")
for x1 in [0, 1]:
    for x2 in [0, 1]:
        output = perceptron(x1, x2, w1, w2, b)
        print(f"NAND({x1}, {x2}) = {output}")

Output:

The code correctly predicts the NAND gate outputs for all input combinations. The perceptron outputs matches expected truth table.