The modern digital logic technology does not yet satisfy the speed requirements of real-time DSP circuits due to synchronized operation of multiplication and accumulation. This operation degrades DSP performance. Therefore, the double-base number system (DBNS) has emerged in DSP system as an alternative methodology because of fast multiplication and hardware simplicity. In this paper, authors propose a novel multiplication architecture. One operand is an output of a flash analog-to-digital converter (ADC) in DBNS format, while the other operand is a coefficient in the IEEE standard floating-point number format. The DBNS digital output from ADC is produced through a new double base number encoder (DBNE). The multiplied output is in the format of the IEEE standard floating-point number (FPNS). The proposed circuits process multiplication and conversion together. Compared to a typical multiplier that uses the FPNS, the proposed multiplier also consumes 45% less gates, and 44% faster than the FPNS multiplier on Spartan-3 FPGA board. The design is verified with FIR filter applications.