Multiplication is one of the most basic processes, in digital signal processing applications. To process the instructions, most processors require multiplication. Because multipliers are employed in almost all arithmetic operations, they consume the majority of time and power. As a nutshell, the multiplier's efficiency is critical in terms of enhancing processor performance. The array multiplier is one of the most efficient multipliers since it is both quick and simple. However, power consumption is high. The basic components of an array multiplier are adders. The multiplier's efficiency will improve if the adders are much more efficient. The prior study used Complementary Metal Oxide Semiconductor (CMOS) to construct a Quaternary Carry-Lookahead Adder (CLA) that substitutes the adder circuit in the array multiplier. Quaternary number system circuits are quicker than binary number system circuits and can execute arithmetic operations without carry. However, Quaternary circuits take up more space. As a solution, the Quaternary Carry Increment Adder (CIA) is proposed. The proposed adder consumes less power and occupies less area than the existing Quaternary CLA. In the array multiplier, the Quaternary CIA substitutes the Quaternary CLA. This helps to lower the multiplier's power and area consumption. Tanner EDA tool is used to designing the circuits and were simulated with 180 nm technology. Various parameters such as delay, power and power-delay product of the existing and the proposed are measured and compared.