Chaotic systems have been applied in many applications involving instrumentation and measurements, such as in sensors and control systems, due to their pseudorandom proprieties. However, reproducing chaos in digital systems is challenging because of the dynamical degradation of chaotic digital systems and, consequently, their intrinsic periodic orbits. Many techniques have been used to guarantee a sufficiently large period, making them suitable for such applications. Nevertheless, few articles pay attention to the effects of using different numerical representations on chaos degradation and, at the same time, keeping key design parameters, such as few logical resources and power consumption. Thus, this article aims to provide a new hardware architecture for a chaos-based pseudorandom number generator (PRNG) using the Half-Unit-Biased (HUB) format for fixed-point numbers by bi-coupling the tent map in conjunction with the Bernoulli map, causing a significant impact on its logical resources and performance. Results show that the HUB format is more effective than the standard fixed-point numerical representation and that the proposed approach is chaotic, with pseudorandomness.