This paper addresses the proposal of improved logarithmic number system (LNS) with extended co-transformation and memory efficient second-degree Newton interpolator. Since the current interpolation with extension requires 4 look-up tables (LUTs), improvement is proposed to achieve requirement by employing only 3 LUTs with small silicon area. It was found that with the proposed extended co-transformation, a set of interpolation LUT that covered region-1 < r <-0.5 could be eliminated. Results from GNU simulator indicated that the maximum error for the proposed Newton interpolation was 9% lower compared to other current interpolators, although the total memory was unsatisfactory. An Implementation shows an efficient memory for a new LNS system, hence benefited for a dynamic real-time computation
