In this article, programmable Josephson voltage standard (PJVS) is used for static and dynamic analog-to digital converter (ADC) characterization. A mathematical tool for investigating the quantum state of the measurement is given. The model function of static gain is derived for uncertainty evaluation. The measured integral nonlinearity (INL) of the ADC is presented. The measured static gain versus time is presented. Dynamic integrating ADC (IADC) characterization using PJVSis described. The gain difference between static and dynamic gains is investigated up to 500 Hz, also at small integration times for different sampling conditions. The measurement errors of dynamic gain are evaluated by the circuit analysis of the stray components in the measurement setup, noises, and spectrum estimation of the results. An example of uncertainty estimation by the work done is given. The main contribution of the presented work is to use the gain difference between the static and dynamic gain parameters for establishing direct traceability between SI(International System of Units) and digital metrology.