At just 4 bits, there are only 16 possible numbers. It becomes lookup table territory - and there is no need to have the numbers on your numberline be linearly or exponentially spaced - you can assign them arbitarily. For example, you could have a number system consisting of: (+-) 0.5, 1, 2, 3, 5, 10, 1000, 1000000 - getting some nice accuracy in the middle of the number line where you expect most values to lie, plus some extreme values so convergence doesn't take forever if some big activation/gradient needs to be propagated.