Here is a MATLAB program to implement logic functions using a McCulloch-Pitts neuron: % McCulloch-Pitts neuron for logic functions % Inputs x1 = 1; x2 = 0; % Weights w1 = 1; w2 = 1; % Threshold theta = 2; % Net input net = x1*w1 + x2*w2; % Activation function if net >= theta y = 1; else y = 0; end % Output disp(y) This implements a basic AND logic gate using a McCulloch-Pitts neuron.

1. McCulloch-Pitts Neuron
Dr. Pravat Kumar Rout
Department of EEE, ITER, SOA University

2. Theory

4. Warren S. McCulloch
The McCulloch-Pitts Neuron was the
earliest neural network discovered in
1943.
The weights associated with
communication links may be
excitatory (weights are positive) or
inhibitory (weights are negative)
A threshold activation function plays
a major role in the M-P neuron. If the
net input is greater than the sum of
the input signals, the neuron fires.
Mostly used in the logic functions.
The activation of M-P neuron is
always binary in nature.
It consists of a number of input units
connected to a single output unit.

5. Salient features of McCulloch-Pitts artificial neuron

6. Architecture

8. Q1. For the network shown in Figure 1, calculate the weights are net input to the output neuron.
Solution: The given neural net consists of three input neurons and one output neuron. The inputs
and weights are
[𝑥1, 𝑥2, 𝑥3] = [0.3,0.5,0.6]
𝑤1, 𝑤2, 𝑤3 = [0.2,0.1, −0.3]
The net input can be calculated as
𝑦𝑖𝑛 = 𝑥1𝑤1 + 𝑥2𝑤2 + 𝑥3𝑤3
= 0.3 × 0.2 + 0.5 × 0.1 + 0.6 × −0.3
= 0.06 + 0.05 − 0.18 = −0.07
Example-1

9. Q2. Calculate the net input for the network shown in Figure 2 with bias included in the network.
Solution: The given net consists of two input neurons a bias and an output neuron. The inputs are
x1, x2 = 0.2,0.6 and the weights are [w1, w2]=[0.3,0.7]. Since the bias is included b=0.45 and bias
input x0is equal to 1. The net input is calculated as
yin= b + x1w1 + x2w2
= 0.45 + 0.2 × 0.3 + 0.6 × 0.7
= 0.45 + 0.06 + 0.42 = 0.93
Therefore, yin = 0.93is the net input.
Example-2

10. Q3. Obtain the output of the neuron Y for the network shown in Figure 3 using activation function
as: (1)binary sigmoidal and (ii) bipolar sigmoidal.
Solution: The given network has three neurons with bias and output neuron. These form a single layer
network. The inputs ere given as x1, x2, x3 = 0.8,0.6,0.4 and the weights are [w1, w2, w3]=[0.1,0.3,-0.2]
with bias b=0.35 (its input is always 1). The net input to the output neuron is
𝑦𝑖𝑛 = 𝑏 + ෍
𝑖=1
𝑛
𝑥𝑖𝑤𝑖
[n=3, because only 3 input neurons are given]
= b + x1 w1 + x2w2 + x3w3
= 0.35 + 0.8 × 0.1 + 0.6 × 0.3 + 0.4 × −0.2
= 0.35 + 0.08 + 0.18 − 0.08 = 0.53
(i)For binary sigmoidal activation function,
𝑦 = 𝑓 𝑦𝑖𝑛 =
1
1+𝑒−𝑦𝑖𝑛
=
1
1+𝑒−0.53 = 0.625
(ii) For bipolar sigmoidal activation function,
𝑦 = 𝑓 𝑦𝑖𝑛 =
2
1+𝑒−𝑦𝑖𝑛
− 1 =
2
1+𝑒−0.53 − 1 = 0.259
Example-3

11. Example-4: M-P Neuron to implementation the
logical AND operation

12. Example-5: M-P Neuron to implementation
the logical OR operation

13. Example-6: M-P Neuron to implementation the
logical AND-NOT operation

14. Example-7: M-P Neuron to implementation
the logical XOR operation

15. Assignment
Write down a suitable MATLAB program for implementing logic functions using M-P
neuron?