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

In the field of Machine Learning, the Perceptron is a Supervised Learning Algorithm for binary classifiers. The Perceptron Model implements the following function: For a particular choice of the weight vector and bias parameter , the model predicts output for the corresponding input vector . XOR logical function truth table for 2-bit binary variables, i.e, the input vector and the corresponding output We can observe that, Designing the Perceptron Network:

1. Step1: Now for the corresponding weight vector of the input vector to the AND and OR node, the associated Perceptron Function can be defined as: [Tex]$\boldsymbol{\hat{y}_{2}} = \Theta\left(w_{1} x_{1}+w_{2} x_{2}+b_{OR}\right)$ [/Tex]

2. Step2: The output from the AND node will be inputted to the NOT node with weight and the associated Perceptron Function can be defined as: 3. Step3: The output from the OR node and the output from NOT node as mentioned in Step2 will be inputted to the AND node with weight . Then the corresponding output is the final output of the XOR logic function. The associated Perceptron Function can be defined as:  For the implementation, the weight parameters are considered to be and the bias parameters are . Python Implementation:

## Python3

 # importing Python library import numpy as np   # define Unit Step Function def unitStep(v):     if v >= 0:         return 1     else:         return 0   # design Perceptron Model def perceptronModel(x, w, b):     v = np.dot(w, x) + b     y = unitStep(v)     return y   # NOT Logic Function # wNOT = -1, bNOT = 0.5 def NOT_logicFunction(x):     wNOT = -1     bNOT = 0.5     return perceptronModel(x, wNOT, bNOT)   # AND Logic Function # here w1 = wAND1 = 1,  # w2 = wAND2 = 1, bAND = -1.5 def AND_logicFunction(x):     w = np.array([1, 1])     bAND = -1.5     return perceptronModel(x, w, bAND)   # OR Logic Function # w1 = 1, w2 = 1, bOR = -0.5 def OR_logicFunction(x):     w = np.array([1, 1])     bOR = -0.5     return perceptronModel(x, w, bOR)   # XOR Logic Function # with AND, OR and NOT   # function calls in sequence def XOR_logicFunction(x):     y1 = AND_logicFunction(x)     y2 = OR_logicFunction(x)     y3 = NOT_logicFunction(y1)     final_x = np.array([y2, y3])     finalOutput = AND_logicFunction(final_x)     return finalOutput   # testing the Perceptron Model test1 = np.array([0, 1]) test2 = np.array([1, 1]) test3 = np.array([0, 0]) test4 = np.array([1, 0])   print("XOR({}, {}) = {}".format(0, 1, XOR_logicFunction(test1))) print("XOR({}, {}) = {}".format(1, 1, XOR_logicFunction(test2))) print("XOR({}, {}) = {}".format(0, 0, XOR_logicFunction(test3))) print("XOR({}, {}) = {}".format(1, 0, XOR_logicFunction(test4)))

Output:

XOR(0, 1) = 1
XOR(1, 1) = 0
XOR(0, 0) = 0
XOR(1, 0) = 1

Here, the model predicted output ( ) for each of the test inputs are exactly matched with the XOR logic gate conventional output ( ) according to the truth table. Hence, it is verified that the perceptron algorithm for XOR logic gate is correctly implemented.

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