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In this paper mathematical models for digital integrators operating with multidigit increments are given, and the discretization error analysis of their linear connections is studied. The integration methods considered are linear multistep integration methods; some examples are studied in detail. Linear digital differential analyzer (DDA) connections are defined, and their use in connection with the numerical solution of the initial value problem is explained. Finally, the discretization error in these linear DDA connections has been analyzed in detail; the theoretical results have also been verified experimentally.