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.