Current trend of downscaling CMOS transistor dimensions is increasing the liability of digital circuits to be easily affected by noise. The resulting unexpected behaviour of our digital devices is due to the low supply voltage of these downscaled circuit elements. Though the low supply voltage decreases the power dissipation of a circuit to a great extent, it decreases the signal to noise ratio as well. The need to transform the conventional logic gates into modified ones having the same functionality but are highly noise-tolerant is catered by the technique Markov Random Field (MRF) modelling proposed in 1. This paper contributes towards explaining MRF design in a simplified form, proves the error tolerant capability of MRF circuits by simulations performed in Cadence (simulation software) and finally proposes an improvement in the design of 1. ©2010 IEEE.