I am learning the backpropagtion algorithm, and would like to clarify some concepts.
Suppose my training data set consists of 20-dimensional bit strings that are classified into 5 different classes. Then my neural net has 20 inputs, and 5 outputs:
10000 01000 00100 00010 00001
Is this correct? What if some new test data yields something like $11000$. How does one interpret this? The data can be in class 1 or 2?
Now let's consider a slightly different problem: Suppose I have inputs consisting of 20-dimensional bit strings, and their outputs are 5-dimensional bit strings. For example,
00000000001111111111 --> 01001 11111000001111100000 --> 11000
I want a network to make these sorts of predictions. So my network should still have 20 inputs, but can I still just use 5 outputs? Following the first example, it looks like I should technically have $2^5$ outputs, each corresponding to one of the possible outputs.
What is the relationship between these classification/prediction problems? Are my setups correct?