The four equations provide us with a way of computing the gradients of the cost function. Let us write this out in the form of an algorithm.
First, we set up the input data \boldsymbol{x} and the activations \boldsymbol{z}_1 of the input layer and compute the activation function and the pertinent outputs \boldsymbol{a}^1 .
Secondly, we perform then the feed forward till we reach the output layer and compute all \boldsymbol{z}_l of the input layer and compute the activation function and the pertinent outputs \boldsymbol{a}^l for l=1,2,3,\dots,L .
Notation: The first hidden layer has l=1 as label and the final output layer has l=L .