  A complete analytical prescription is given to perform three basic (OR, AND,
NOT) and two universal (NAND, NOR) logic gates at nano-scale level using simple
tailor made geometries. Two different geometries, ring-like and chain-like, are
taken into account where in each case the bridging conductor is coupled to a
local atomic site through a dangling bond whose site energy can be controlled
by means of external gate electrode. The main idea is that when injecting
electron energy matches with site energy of local atomic site transmission
probability drops exactly to zero, whereas the junction exhibits finite
transmission for other energies. Utilizing this prescription we perform logical
operations, and, we strongly believe that the proposed results can be verified
in laboratory. Finally, we numerically compute two-terminal transmission
probability considering general models and the numerical results matches
exactly well with our analytical findings.
