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Nano-Electro-Mechanical Switches (NEMS) offer the prospect of improved energy-efficiency in digital circuits due to their near-zero subthreshold leakage and extremely low subthreshold swing values. Among the different approaches of implementing NEMS, laterally-actuated double-gate NEMS devices have attracted much attention as they provide unique and exciting circuit design opportunities. For instance, this paper demonstrates that compact XOR/XNOR gates can be implemented using only two such NEMS transistors. While this in itself is a major improvement, its implications for minimizing Boolean functions using Karnaugh maps (K-maps) are even more significant. In the standard K-map technique, which is used in digital circuit design, adjacent “1s” (minterms) are grouped only in horizontal and/or vertical directions; the diagonal (or zig-zag) grouping of adjacent “1s” is not an option due to the absence of compact XOR/XNOR gates. However, this work demonstrates, for the first time ever, that in lateral double-gate NEMS-based circuits, grouping of minterms is possible in horizontal and vertical as well as diagonal fashions. This is because the diagonal groupings of minterms require XOR/XNOR operations, which are available in such NEMS-based circuits at minimal costs. This novel design paradigm facilitates more compact implementations of Boolean functions and thus, considerably improves their energy-efficiency. For example, a lateral NEMS-based full-adder is implemented using less than half the number of transistors, which is required by a CMOS-based full-adder. Furthermore, circuit simulations are performed to evaluate the energy-efficiencies of the NEMS-based 32bit carry-save adders compared to their standard CMOS-based counterparts.