OR Gate Model using Perceptron

Let’s mathematically demonstrate how to train a perceptron to implement the OR gate. The OR gate produces an output of 1 if at least one of its inputs is 1. We’ll follow the Perceptron algorithm to find the weights and bias for this logic gate.

Problem Description (OR Gate):

The OR Gate has the following truth table:

Perceptron Model:

The Perceptron model predicts:

• If (Wx + b > 0), then (y' = 1).
• If (Wx + b <= 0), then (y' = 0).

Weights and Bias:

• Initialize weights (w_1) and (w_2) as 1.
• Set bias (b) as -0.5.

Calculations:

For each row in the OR truth table:

• Row 1 (x1=0, x2=0):
• (w_1 . x1 + w_2 . x2 + b = 0 + 0 - 0.5 = -0.5)
• Since (-0.5 <= 0), (y’ = 0).

• Row 2 (x1=0, x2=1):

• (w_1 . x1 + w_2 . x2 + b = 0 + 1 - 0.5 = 0.5)
• Since (0.5 > 0), (y’ = 1).

• Row 3 (x1=1, x2=0):

• (w_1 . x1 + w_2 . x2 + b = 1 + 0 - 0.5 = 0.5)
• Since (0.5 > 0), (y’ = 1).

• Row 4 (x1=1, x2=1):

• (w_1 . x1 + w_2 . x2 + b = 1 + 1 - 0.5 = 1.5)
• Since (1.5 > 0), (y’ = 1).

Conclusion:

The perceptron model for the OR gate is: [ y’ = x1 + x2 - 0.5 ]