# Perceptron Algorithm for Logic Gate with 3-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 .
The logical function truth table of AND, OR, NAND, NOR gates for 3-bit binary variables, i.e, the input vector and the corresponding output        0 0 0 0 0 1 1
0 0 1 0 1 1 0
0 1 0 0 1 1 0
0 1 1 0 1 1 0
1 0 0 0 1 1 0
1 0 1 0 1 1 0
1 1 0 0 1 1 0
1 1 1 1 1 0 0

Now for the corresponding weight vector of the input vector , the associated Perceptron Function can be defined as:  For the implementation, considered weight parameters are and the bias parameter is for every logic gates-      1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -2 -0.9 3 1

Python Implementation:

 # importing python library  import numpy as np     # sigmoid activation function  def activationFunction(model, type ="sigmoid"):     return {         "sigmoid": 1 / (1 + np.exp(-model))     }[type]     # designing perceptron model  def perceptronModel(weights, inputs, bias):     model = np.add(np.dot(inputs, weights), bias)     logic = activationFunction(model, type ="sigmoid")     return np.round(logic)     # computation model  def compute(data, logicGate, weights, bias):     weights = np.array(weights)     output = np.array([ perceptronModel(weights,                datum, bias) for datum in data ])     return output     # Print Output  def printOutput(dataset, name, data):     print("Logic Function: {}".format(name.upper()))     print("X1\tX2\tX3\tY")     toPrint = ["{1}\t{2}\t{3}\t{0}".format(output, *datas)                  for datas, output in zip(dataset, data)]     for i in toPrint:         print(i)     # main function  def main():     # 3 bit binary data     dataset = np.array([       [0, 0, 0],       [0, 0, 1],       [0, 1, 0],       [0, 1, 1],       [1, 0, 0],       [1, 0, 1],       [1, 1, 0],       [1, 1, 1]     ])        # Parameters of every Logic Gates     # weight parameters: w1, w2, w3     # bias parameter: b     logicGate = {         "and": compute(dataset, "and", [1, 1, 1], -2),         "or": compute(dataset, "or", [1, 1, 1], -0.9),         "nand": compute(dataset, "nand", [-1, -1, -1], 3),         "nor": compute(dataset, "nor", [-1, -1, -1], 1)     }     for gate in logicGate:         printOutput(dataset, gate, logicGate[gate])     if __name__ == '__main__':     main()

Output:

Logic Function: AND
X1    X2    X3    Y
0    0    0    0.0
0    0    1    0.0
0    1    0    0.0
0    1    1    0.0
1    0    0    0.0
1    0    1    0.0
1    1    0    0.0
1    1    1    1.0
Logic Function: OR
X1    X2    X3    Y
0    0    0    0.0
0    0    1    1.0
0    1    0    1.0
0    1    1    1.0
1    0    0    1.0
1    0    1    1.0
1    1    0    1.0
1    1    1    1.0
Logic Function: NAND
X1    X2    X3    Y
0    0    0    1.0
0    0    1    1.0
0    1    0    1.0
0    1    1    1.0
1    0    0    1.0
1    0    1    1.0
1    1    0    1.0
1    1    1    0.0
Logic Function: NOR
X1    X2    X3    Y
0    0    0    1.0
0    0    1    0.0
0    1    0    0.0
0    1    1    0.0
1    0    0    0.0
1    0    1    0.0
1    1    0    0.0
1    1    1    0.0


Here, the model predicted output ( ) for each of the test inputs are exactly matched with the AND, OR, NAND, NOR logic gates conventional output ( )s according to the truth table for 3-bit binary input.
Hence, it is verified that the perceptron algorithm for all these logic gates is correctly implemented.

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