This study proposes a novel double-base log encoder (DBLE) for flash Analog-to-Digital converters (ADCs). Analog inputs of flash ADCs are represented in logarithmic number systems with bases of 2 and 3 at the outputs of DBLE. A look up table stores the sets of exponents of base 2 and 3 values. This algorithm improves the performance of a DSP (Digital Signal Processor) system that takes outputs of a flash ADC, since the double-base log number representation does multiplication operation easily within negligible error range in ADC. We have designed and implemented 6 bits DBLE implemented with ROM (Read-Only Memory) architecture in a $0.18;{mu}m$ CMOS technology. The power consumption and speed of DBLE are better than the FAT tree and binary ROM encoders at the cost of more chip area. The DBLE can be implemented into SoC architecture with DSP to improve the processing speed.