A fast moving average would be something like this:

mav = (1-alpha)*mav + alpha * new_data;

where 0<alpha<1 as a weight for new observations. The smaller alpha is, the longer memory mav has of historical data.

If you pick alpha to be 1/2^n, the math gets considerably easier as you can simply shift. For example, for alpha = 1/16:

mav = mav + (new_data - mav) / 16.

essentially, 1 subtraction, 1 shift, 1 increment.