Inexact computing is an attractive concept for digital signal processing at the submicron regime. This paper proposes 2-bit inexact adder cell and further escalate to 4-bit, and 8-bit inexact adder and error metrics have been evaluated mathematically for such adder cells. The approximated design has been proposed through the simplification of the K-Maps, which leads to a substantial reduction in the propagation delay as well as energy consumption. The proposed design has been verified through the Cadence Spectre and performance parameters (such as delay, power consumption) have been evaluated through CMOS gpdk45 nm technology. Furthermore, the proposed design has been applied to image de-noising application where the performance of the images like Peak Signal to Noise Ratio (PSNR), Normalized Correlation Coefficient (NCC) and Structural Similarity Index (SSIM) has been analyzed through MATLAB, which offer the substantial improvement from its counterpart.