The one-dimensional map represented by the Bernoulli shift is a candidate of true random number generators. However, no computer with finite-word-length can precisely realize the Bernoulli shift. The M-sequence is shown to be one of finite-word-length approximations to the Bernoulli shift in the sense that the many-to-many map generated by M-sequence is the same as the finite-word-length realization of the iterated Bernoulli shift.