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The averaging technique is used in flash analog-to-digital converters to reduce nonlinearities resulting from random offset voltages of the pre-amplifiers, which stand before the comparators. The main contribution of this paper is to provide further insight into this technique, through exact closed-form expressions obtained for the output voltage, gain, integral nonlinearity and differential nonlinearity in averaged pre-amplifiers. These theoretical results are compared with HSPICE simulations, and a very good agreement is found. Finally an automatic design procedure is described, which is based on the expressions derived, and a design example is given.