How can information be encoded and decoded in populations of adapting neurons? How can this code be read? To answer these questions quantitatively is to provide a mathematical expression relating the neuronal activity to the external stimulus. And conversely: relating the external stimulus to the neuronal activity. Although such equations are known and well accepted for the special problem of relating external stimulus to a time series of action potentials, the problem of relating the external stimulus to the activity of a population has proven more difficult. There is a bothersome gap between the dynamics of single neurons and the dynamics of populations, particularly when the neuronal population constantly adapts to the external stimulus. The neural code of adapting populations is ambiguous because it is possible to observe a range of population activities in response to a given instantaneous input. Somehow the ambiguity is resolved by elements of the population history, but how precisely? In this article we use approximation methods to provide mathematical expressions that describe the encoding and decoding of external stimulus in adapting populations. The theory presented here helps to bridge the gap between the dynamics of single-neurons and that of populations.