Adders are one of the essential blocks of Arithmetic Logic Unit (ALU), addressing the memory, table indices and many more such types of applications. The speed of the adder unit more often decides the performance of CPU (Central Processing Unit) and GPU (Graphics Processing Unit) for graphics applications. The high-speed design is a very important performance parameter speed that too with less implementation area and low power consumption. In this paper, the author proposes a novel 32-bit Residue Hybrid Adder (RHA) using the Residue Number System (RNS) and implemented using a Hybrid CMOS/PTL logic style. An RNS has the advantage of representing a large integer using a set of few smaller integers to make computation more efficient and effective. On the other side, parallel prefix adders provide faster execution time as it performs the operation in parallel. With our paper, it is evident that RHA gives better performance in terms of delay, power consumption and area for arithmetic operations. The experimental analysis has been performed using the EDA tool on 45-nm CMOS technology. The power, delay and power delay product (PDP) performance parameters are compared with the existing adders and the results show that, thanks to smaller modules, proposed units have both smaller area and delay by up to 45% and 41%, and, consequently, they allow achieving up to over 46% power saving, respectively.