Can Convolutional Neural Networks (CNN) be represented by a Mathematical formula?

Let's say that I already trained my CNN. Is there anyway of my ouput to be represented as a formula just like a perceptron can (x1w1 + x2w2 + ... = PREDICTION).

It does not matter if the formula is more complicated than the perceptron one, but in general would it be possible to train a CNN in Python or Matlab, get the weights and create an arithmetic, exponential, whatever formula made with those acquired weights?

With that, after training, I would be able to apply my new values to this formula and get a desired output/prediciton values.

I want to do this because I am trying classify in a PIC32 (a low cost microchip) which I think that does not have the capacity to perform a CNN within itself.

Or, for example, should I pursue the idea of some sort of "C library" that can do CNNs?