Boolean averaging in an analog-to-digital converter

The operation of an analog-to-digital converter with sigma-delta modulation and leaky integration is described in terms of Boolean averaging by the methods of symbolic dynamics. The output of an analog-to-digital converter is a Cantor ladder of the constant input signal. This result, known until recently only for periodic modes, is extended to arbitrary modes. The output of an analog-to-digital converter for varying inputs is estimated. In the limiting operation mode, a pulse-modulated control system functions in the same way as an analog-to-digital converter.