# Implementation of Perceptron Algorithm for NOR 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 . NOR logical function truth table for 2-bit binary variables, i.e, the input vector and the corresponding output
0 0 1
0 1 0
1 0 0
1 1 0
We can observe that, Now for the corresponding weight vector of the input vector to the OR node, the associated Perceptron Function can be defined as:

Later on, the output of OR node is the input to the NOT node with weight . Then the corresponding output is the final output of the NOR logic function and the associated Perceptron Function can be defined as:

For the implementation, considered weight parameters are and the bias parameters are . Python Implementation:
 # 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)   # 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)   # NOR Logic Function # with OR and NOT   # function calls in sequence def NOR_logicFunction(x):     output_OR = OR_logicFunction(x)     output_NOT = NOT_logicFunction(output_OR)     return output_NOT   # 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("NOR({}, {}) = {}".format(0, 1, NOR_logicFunction(test1))) print("NOR({}, {}) = {}".format(1, 1, NOR_logicFunction(test2))) print("NOR({}, {}) = {}".format(0, 0, NOR_logicFunction(test3))) print("NOR({}, {}) = {}".format(1, 0, NOR_logicFunction(test4)))

Output:
NOR(0, 1) = 0
NOR(1, 1) = 0
NOR(0, 0) = 1
NOR(1, 0) = 0

Here, the model predicted output () for each of the test inputs are exactly matched with the NOR logic gate conventional output () according to the truth table for 2-bit binary input. Hence, it is verified that the perceptron algorithm for NOR logic gate is correctly implemented.

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