A multiplication apparatus including a multiplier and multiplicand extractor for dividing the multiplicand into partial multiplicands and dividing the multiplier into partial multipliers, and for generating partial input pairs by combining the partial multiplicands with the partial multipliers, and a multiplication executor including identical partial multiplication modules for receiving the partial input pairs and outputting partial carries and partial products. The apparatus further includes an output generator for combining the partial carries with the partial products according to the execution instruction to generate a final output. For simple multiplications, each of the partial multiplication modules can pass data to and from an adjacent partial multiplication module to calculate the partial carry and the partial product, and pass bits exceeding its own multiplication coverage.