Question

1. Neurons: Please construct a Neural Network for the following logic, NAND

Truth table for NAND function
i1	i2	output
0	0	1
0	1	1
1	0	1
1	1	0

Answer 1

First, we need to know that the Perceptron algorithm states that:

Prediction (y`) = 1 if Wx+b > 0 and 0 if Wx+b ≤ 0

Also, the steps in this method are very similar to how Neural Networks learn, which is as follows;

• Initialize weight values and bias
• Forward Propagate
• Check the error
• Backpropagate and Adjust weights and bias
• Repeat for all training examples

Now that we know the steps, let’s get up and running:

NAND Gate

From the diagram, the NAND gate is 0 only if both inputs are 1.

Row 1

• From w1x1+w2x2+b, initializing w1 and w2 as 1, and b as -1, we get;

x1(1)+x2(1)-1

• Passing the first row of the NAND logic table (x1=0, x2=0), we get;

0+0-1 = -1

• From the Perceptron rule, if Wx+b≤0, then y`=0. This row is incorrect, as the output is 1 for the NAND gate.
• So we want values that will make input x1=0 and x2 = 0 to give y` a value of 1. If we change b to 1, we have;

0+0+1 = 1

• From the Perceptron rule, this works.

Row 2

• Passing (x1=0, x2=1), we get;

0+1+1 = 2

• From the Perceptron rule, if Wx+b > 0, then y`=1. This row is also correct (for both row 2 and row 3).

Row 4

• Passing (x1=1, x2=1), we get;

1+1+1 = 3

• This is not the expected output, as the output is 0 for a NAND combination of x1=1 and x2=1.
• Changing values of w1 and w2 to -1, and value of b to 2, we get;

-1-1+2 = 0

• It works for all rows.

Therefore, we can conclude that neural network  to achieve a NAND gate, using the Perceptron algorithm is;

-x1-x2+2