Additive White Gaussian Noise (AWGN) is common to every communication channel. It is statistically random radio noise characterized by a wide frequency range with regards to a signal in communication channels. In this paper, AWGN signal is generated through design an analogue circuit method, and then the multiple recursive method is also used to generate random data signal that is used for testing by Lyapunov exponent. Furthermore an algorithm for software generating of Additive White Gaussian Noise is presented. Lyapunov exponent test for chaos is used to distinguish between regular and chaotic dynamics of the generated data by the two methods. Simulation results are enhanced with the use of Microcontroller chip, since the hardware of the application is implemented by microcontroller-embedded system to obtain computerized noise generator. The results show that the generated AWGN signal by the analogue method and the multiple recursive method is chaotic which implies the random like-noise behavior.