4 Neurons to Decide 10 Digits I am trying to solve this algorithm exercises (http://neuralnetworksanddeeplearning.com/chap1.html#exercise_513527) in Michael Nielson's online book: Neural Networks and Deep Learning (http://neuralnetworksanddeeplearning.com/chap1.html#complete_zero). 

In another word, he says that there is a way to use four neurons to decide 10 digits on top of of the last hidden layer (which consists of 10 neurons and decides 10 digits separately with a high correct rate).

However I couldn't figure out the way. Do you have any idea about this? I look forward to your idea. Any help is appreciated.
You could use 4 neurons to produce a 4-bit output, which then represents the digit in binary.  A digit in the range 0-9 can be expressed in binary as a 4-bit number.

However, classification accuracy might potentially be worse than the standard method of 10 output neurons with a softmax layer.