Complex numbers play a vital role in the implementation of a wide number of Digital Signal Processing (DSP) algorithms. Since they are represented as two separate components (real and imaginary), the algorithms increased the number of computations. In this letter, we present an improved approach that reduces the number of computations by integrating the computation of the radix-2 Fast Fourier Transform (FFT) with the Distributed Arithmetic (DA) and Complex Binary Number System (CBNS). Further, the proposed architecture replaces multipliers with the use of adders and shifters, which considerably decrease the design area. Although more adders are needed to implement the new DA-CBNS proposed architecture, when compared to the traditional radix-2 FFT and DA or CBNS -based FFT algorithms, results show that the proposed design yields an increase in operating frequency, and a reduction in size, memory usage, and power consumption.