This problem is adapted from an exercise in chapter 1 There is a way of determining the bitwise representation . Suppose you have a neural network with 3 layers. The first layer is the input layer with 784 neurons encoding the 28*28 pixel values of an image of a handwritten octal digit (0,1,,7). The second layer consists of 40 sigmoid neurons and the final layer consists of 8 sigmoid neurons each with their own weights and biases. The neurons in adjacent layers are fully connected. We can add a fourth layer with three sigmoid neurons to this network to convert the output from the third layer into a binary representation out of the fourth layer (000 for digit 0, 001 for digit 1, ..., 111 for digit 7; the three binary bits are to be the outputs of the three sigmoid neurons of the fourth layer). Find a set of 24 weights (wij, i=1,2,3, j=1,2,,8 represents the weight from the jth neuron of the third layer to the ith neuron of the fourth layer) and 3 biases (w11,..,w18,w21,,w28,w31,,w38,b1,b2,b3) for the new output layer to achieve the goal of binary representation. Assume that the first 3 layers of neurons are such that the correct output in the third layer (i.e., the old output layer) has activation almost equal to 1 (or at least 0.9999), and incorrect outputs have activation almost equal to 0 (or less than 0.0001).