Fast conversion from residue numbers to conventional weighted numbers is necessitated in magnitude comparison, sign determination and overflow detection in usual computing. These are especially important applications in the general division for a residue number system. In the process of general division, for example, the sign of the residue must be known, and therefore the conversion procedure must be taken into account in order to obtain the magnitude of two operands for each step. This paper presents an optimal matched and parallel scheme for mixed-radix digit conversion to improve the speed of conversion, and reduce the area and power dissipation. This optimal matched mixed-radix converter can have the dynamic range of 300 bits (30 moduli) in length with a conversion time of 50 ns (2 clock cycles).