Deep Learning - How to represent Boolean functions with the McCulloch-Pitts Neuron

Introduction

In this tutorial we will cover how to represent boolean functions with the McCulloch-Pitts Neuron. We look at the boolean functions AND, OR and NOT.

McCulloch-Pitts Neuron

We have already explained how the McCulloch-Pitts Neuron works in another post. If you haven't seen it yet, check it out.

Deep Learning - How the McCulloch-Pitts Neuron works

Introduction In this tutorial we will cover the very first and the simplest mathematical neuron model in history - the McCulloch-Pitts Neuron. We look at the architecture and functionality. History The McCulloch-Pitts-Neuron is the simplest form of a neuron model and was published in 1943 by Warren McCulloch and Walter

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Now let's cover how the McCulloch-Pitts Neuron can represent boolean functions. The main elements for modeling the boolean functions are the choice of weights and the threshold value.

AND function

First, we consider the AND function. The truth table for x₁ AND x₂ is as follows:

In the case of the AND function the output is only 1 if both inputs are 1. In all other cases, the output is 0.

Let's cover how the McCulloch-Pitts Neuron must be designed so that the AND function can be represented.