We propose a new type of the Josephson junction A/D converter which allows one to increase the conversion accuracy (characterized by the output bit number N) without using high-precision (

) components. This improvement is possible due to a specific structure of the new device including a fast low-bit (

) input A/D converter and several digital differentiation/integration stages. We discuss general properties of this device and possible realization of its main components in the Josephson technology. Estimates show that at relatively low signal frequencies an additional digital stage (1f filter) can improve drastically the converter performance making it considerably more accurate than any other A/D converter proposed earlier.