The Fast Fourier Transform (FFT) and its inverse (IFFT) are very important algorithms in digital signal processing and communication systems. Radix-2 FFT algorithm is the simplest and most common form of the Cooley-Tukey algorithm.Radix-2 2 FFT algorithm is an attractive algorithm having same multiplicative complexity as radix-4 algorithm, but retains the simple butterfly structure of radix-2 algorithm. These algorithms have been developed using Verilog hardware description language and implemented on Spartan6 FPGA.