Before introducing research results, the authors present a complete and well described survey of the major results of the integer multiplication problem from the point of view of the direct VLSI circuit realization. Then they define a class of optimal VLSI multipliers of n bit integers, where the optimality is studied according to the AT² VLSI measure of complexity. Execution time for the new multipliers varies in the range of [(logn), 0(:.PC9 :3- Wz:Ln)], while previously defined VLSI circuits, for the same problem, required time in the range [&OHgr;(log²n),0(:.PC9 √Ln)].

The results presented in this paper are relevant, especially from a theoretical point of view. In fact, the problem of VLSI integer multiplication is settled because it is shown that there exists an AT² optimal VLSI multiplier for the entire spectrum of computation time.