  This article presents a vertical multiplication formula for calculating the
multiplication of any two multi-digit integers, which may be not only used to
design the multiplier but also to the mental multiplication. Our algorithm is a
generalization of that of Karatsuba and Offman, but it is superior to the
latter because the latter is not suitable for oral calculation of
multiplication of large integers. These two algorithms are both the vertical
multiplication method, but in our algorithm the horizontal subtraction in stead
of the horizontal addition used in the Kartsuba algorithm makes the involved
numbers are much smaller and their algebraic sum are much smaller too because
the positive and negative numbers probably cancel each other out. Because of
the above advantages, our vertical multiplication formula allows more practical
and efficient multipliers to be designed.
