In the paper, an algorithm called a Constraint algorithm is proposed to solve the fan-in problem occurred in ADC encoding circuits. The Flash ADC architecture uses a double-base number system (DBNS). The DBNS has known to represent the multi-dimensional logarithmic number system (MDLNS) used for implementing the multiplier accumulator architecture of FIR filter in digital signal processing (DSP) applications. The authors use the DBNS with the base 2 and 3 to represent binary output of ADC. A symmetric map is analyzed first, and then asymmetric map is followed to provide addition read DBNS to DSP circuitry. The simulation results are shown for the Double-Base Integer Encoder (DBIE) of the 6-bit ADC to demonstrate an effectiveness of the Constraint algorithm, using $0.18{mu};m$ CMOS technology. The DBIE’s processing speed of the ADC is fast compared to the FAT tree encoder circuit by 0.95 GHz.