The approximate computing has emerged as an appealing approach to minimize energy consumption. By implementing inexact circuits at the transistor level, significant enhancements in various performance metrics such as power consumption, delay, energy, and area can be achieved. Consequently, researchers worldwide have been actively exploring the application of inexact techniques in circuit design. This paper introduces a novel technique for designing low-power digital circuits called extremely low power modified gate diffusion input (ELP-MGDI). This technique combines the principles of Modified Gate Diffusion Input with the utilization of Carbon Nano Tube Field-Effect Transistors (CNTFETs). The Objective of this paper is to enhance the power, delay, and area characteristics of a 4:2 compressor and multiplier by employing ELP-MGDI approach. To achieve this, we conducted thorough analysis and simulations using the Verilog-A simulator 32 nm CNFET technology Stanford University within the Cadence Virtuoso Tool. The results show extremely power, delay reduction and power-delay-product (PDP) of approximate multiplier has been improved by over 99%, and the circuit area has been reduced by 55%. The proposed processing module demonstrates superior performance compared to their conventional counterparts.