Yes, I am familiar with the bitwise sum example demonstrated in "Neural Networks and Deep Learning" by Michael Nielsen.

In Chapter 1 of the book, Nielsen demonstrates how to use a neural network to perform the bitwise sum operation, where the inputs are two binary numbers of length 8 (i.e., 8 bits each), and the output is their sum.

To do this, he constructs a neural network with three layers: an input layer with 16 neurons (i.e., 8 neurons for each input number), a hidden layer with 16 neurons, and an output layer with 8 neurons (i.e., one for each bit of the sum). He uses the sigmoid function as the activation function for each neuron, and trains the network using backpropagation with stochastic gradient descent.

The key insight behind this approach is to treat the bitwise sum operation as a classification problem, where each bit of the output can be either 0 or 1. By using a neural network with sigmoid activation functions, the network can learn to assign the correct output for each bit based on the input.

Nielsen's example is a simple but powerful demonstration of how neural networks can be used to solve a wide range of problems, including those that involve complex logic or decision-making.