We propose an analytical model of the effects of a nonuniform distribution of trapped charge on the electrical characteristics and on the perspectives of 2-bit operation of discrete-trap memories. To keep the model tractable, we consider an idealized nonuniform distribution, represented by a step function, so that the concentration of trapped charge can assume only two possible values in two different regions. Notwithstanding the simplicity of our assumptions, which limits the range of validity of our model to the subthreshold and weak inversion regions of the I-V characteristics, we can investigate a series of important aspects for 2-bit storage of nonvolatile memories. Our model is then validated through comparison with detailed numerical simulations performed with a commercial technology computer-aided design tool, and with the experimental electrical characteristics of nanocrystal flash memories under different bias conditions. Finally, we provide a method, based on our model, to extract an "effective" distribution of trapped charge, in which all charge is uniformly distributed in a localized region close to the drain.