In the field of Machine Learning, the Perceptron is a Supervised Learning Algorithm for binary classifiers. The Perceptron Model implements the following function:
![\[ \begin{array}{c} \hat{y}=\Theta\left(w_{1} x_{1}+w_{2} x_{2}+\ldots+w_{n} x_{n}+b\right) \\ =\Theta(\mathbf{w} \cdot \mathbf{x}+b) \\ \text { where } \Theta(v)=\left\{\begin{array}{cc} 1 & \text { if } v \geqslant 0 \\ 0 & \text { otherwise } \end{array}\right. \end{array} \]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-f98cbf4744582c2b3309f1b0ceb8a313_l3-1.png "Rendered by QuickLaTeX.com")
For a particular choice of the weight vector 
and bias parameter 
, the model predicts output 
for the corresponding input vector 
.
AND logical function truth table for 2-bit binary variables, i.e, the input vector 
and the corresponding output 
–
 |
 |
|
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Now for the corresponding weight vector 
of the input vector , the associated Perceptron Function can be defined as:
![\[$\boldsymbol{\hat{y}} = \Theta\left(w_{1} x_{1}+w_{2} x_{2}+b\right)$\]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-9028cdb4e1fc09398f4e0b8ab8c8a7cc_l3-1.png "Rendered by QuickLaTeX.com")
For the implementation, considered weight parameters are 
and the bias parameter is 
.
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 # AND Logic Function# w1 = 1, w2 = 1, b = -1.5def AND_logicFunction(x): w = np.array([1, 1]) b = -1.5 return perceptronModel(x, w, b) # testing the Perceptron Modeltest1 = np.array([0, 1])test2 = np.array([1, 1])test3 = np.array([0, 0])test4 = np.array([1, 0]) print("AND({}, {}) = {}".format(0, 1, AND_logicFunction(test1)))print("AND({}, {}) = {}".format(1, 1, AND_logicFunction(test2)))print("AND({}, {}) = {}".format(0, 0, AND_logicFunction(test3)))print("AND({}, {}) = {}".format(1, 0, AND_logicFunction(test4))) |
AND(0, 1) = 0 AND(1, 1) = 1 AND(0, 0) = 0 AND(1, 0) = 0
Here, the model predicted output () for each of the test inputs are exactly matched with the AND logic gate conventional output () according to the truth table for 2-bit binary input.
Hence, it is verified that the perceptron algorithm for AND logic gate is correctly implemented.
