Perceptron Algorithm for Logic Gate with 3-bit Binary Input
AND, OR, NAND, NOR
3-bit binary variables
| 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 |
| 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
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