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An approximation to the computation of the base two logarithm of a binary number, realized with binary circuitry, is described. It is known that the logarithm can be obtained approximately from the binary number itself by simple counting and shifting. A method for the reduction of the resulting approximation error by a factor six is given. The same principle can be used for further reduction of the error. The realization involving not only counting and shifting but also binary decision making and addition is described. Technical data about the performance of the constructed computer are given.