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In this paper the model of a system for measuring small currents, which generates the digital signal proportional to the input current, was designed. The analysed measuring system is the part of a larger microelectronic mixed-signal integrated chip (SoC -System on Chip), and it is located between the input sensor and the external digital device. Since the part that mostly contributes to the noise inside the whole measuring chain is at the input of the chain, the measurement method is analyzed to minimize the impact of noise. Because the noise is not definite, the simulation of measurement by the model was made using statistical principles. Performing multiple measurements of the input value (in our example it is current I d ) it is possible to calculate its mean value and standard deviation. It was shown that the measured quantity can be calculated from the mean value and that the standard deviation represents an amount of noise. Depending on the standard deviation it is needed to do either less or more sequential measurements to determine the reliable measured output digital value.