Implementation of Perceptron Algorithm for OR Logic Gate with 2-bit Binary Input

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In the field of Machine Learning, the Perceptron is a Supervised Learning Algorithm for binary classifiers. The Perceptron Model implements the following function:

$\begin{array}{c} \hat{y}=\Theta\left(w_{1} x_{1}+w_{2} x_{2}+\ldots+w_{n} x_{n}+b\right) \\ =\Theta(\mathbf{w} \cdot \mathbf{x}+b) \\ \text { where } \Theta(v)=\left\{\begin{array}{cc} 1 & \text { if } v \geqslant 0 \\ 0 & \text { otherwise } \end{array}\right. \end{array}$

For a particular choice of the weight vector $\boldsymbol{w}$ and bias parameter $\boldsymbol{b}$ , the model predicts output $\boldsymbol{\hat{y}}$ for the corresponding input vector $\boldsymbol{x}$ .

OR logical function truth table for 2-bit binary variables, i.e, the input vector $\boldsymbol{x} : (\boldsymbol{x_{1}}, \boldsymbol{x_{2}})$ and the corresponding output $\boldsymbol{y}$ –

$\boldsymbol{x_{1}}$	$\boldsymbol{x_{2}}$	$\boldsymbol{y}$
0	0	0
0	1	1
1	0	1
1	1	1

Now for the corresponding weight vector $\boldsymbol{w} : (\boldsymbol{w_{1}}, \boldsymbol{w_{2}})$ of the input vector $\boldsymbol{x} : (\boldsymbol{x_{1}}, \boldsymbol{x_{2}})$ , the associated Perceptron Function can be defined as:

$\boldsymbol{\hat{y}} = \Theta\left(w_{1} x_{1}+w_{2} x_{2}+b\right)$

For the implementation, considered weight parameters are $\boldsymbol{w_{1}} = 1, \boldsymbol{w_{2}} = 1$ and the bias parameter is $\boldsymbol{b} = -0.5$ .

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 
  
# OR Logic Function 
# w1 = 1, w2 = 1, b = -0.5 
def OR_logicFunction(x): 
    w = np.array([1, 1]) 
    b = -0.5
    return perceptronModel(x, w, b) 
  
# 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("OR({}, {}) = {}".format(0, 1, OR_logicFunction(test1))) 
print("OR({}, {}) = {}".format(1, 1, OR_logicFunction(test2))) 
print("OR({}, {}) = {}".format(0, 0, OR_logicFunction(test3))) 
print("OR({}, {}) = {}".format(1, 0, OR_logicFunction(test4))) 

Output:

OR(0, 1) = 1
OR(1, 1) = 1
OR(0, 0) = 0
OR(1, 0) = 1

Here, the model predicted output ( $\boldsymbol{\hat{y}}$ ) for each of the test inputs are exactly matched with the OR logic gate conventional output ( $\boldsymbol{y}$ ) according to the truth table for 2-bit binary input.
Hence, it is verified that the perceptron algorithm for OR logic gate is correctly implemented.

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Last Updated : 08 Jun, 2020

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Implementation of Perceptron Algorithm for OR Logic Gate with 2-bit Binary Input

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