Finite word length is a practical limitation when discrete-time systems are implemented by using digital hardware. This restriction degrades the performance of a discrete-time system and may even lead it toward instability. This paper, addresses the stability and disturbance attenuation performance analysis of nonlinear discrete-time systems under the influence of energy-bounded external interferences when such systems are subjected to quantization and overflow effects of fixed point hardware. The proposed methodology, in comparison with previous paper, describes exponential stability for the nonlinear discrete-time systems by considering composite nonlinearities of digital hardware. The proposed criteria that ensure exponential stability and [Formula: see text] performance index for the digital systems under consideration are presented in the form of a set of linear matrix inequalities (LMIs) by exploiting Lyapunov stability theory, Lipschitz condition and sector conditions for different types of commonly used quantization and overflow arithmetic properties, and the results are validated for recurrent neural networks. Furthermore, novel stability analysis results for a nonlinear discrete-time system under hardware constraints can also be observed as a special case of the proposed criteria.