Let's understand how to implement a neural network on a computer by expressing a single neuron mathematically, as follows:

The inputs here are numbers, followed by the computational units. We are familiar with the fact that we do not know the functioning of a biological neuron, but while creating an artificial network, we actually possess the power to build a process. 

Let us build a computational unit that will process the data in two steps as depicted in the previous diagram. The first step will sum all the input values obtained so far, and for the second step, we will apply the sum attained in the previous step to a sigmoid function as depicted in the preceding diagram. 

The purpose of the sigmoid function is to provide the output as 1 when the sum applied is positive, and to give the output as 0 when the sum applied is negative. In this example, the sum of X1, X2, X3, and X4 will be -3, which, when applied to the sigmoid function, will give us the final value of 0.1.

The sigmoid function, which is applied after the sum, is called the activation function, and is denoted by a.