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# 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

001
010
100
110

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 libraryimport numpy as np  # define Unit Step Functiondef unitStep(v):    if v >= 0:        return 1    else:        return 0  # design Perceptron Modeldef perceptronModel(x, w, b):    v = np.dot(w, x) + b    y = unitStep(v)    return y  # NOT Logic Function# wNOT = -1, bNOT = 0.5def NOT_logicFunction(x):    wNOT = -1    bNOT = 0.5    return perceptronModel(x, wNOT, bNOT)  # OR Logic Function# w1 = 1, w2 = 1, bOR = -0.5def 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 sequencedef NOR_logicFunction(x):    output_OR = OR_logicFunction(x)    output_NOT = NOT_logicFunction(output_OR)    return output_NOT  # testing the Perceptron Modeltest1 = 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.