A New Class of Digital Division Methods

This paper describes a class of division methods best suited for use in digital computers with facilities for floating point arithmetic. The division methods may be contrasted with conventional division procedures by considering the nature of each quotient digit as generated during the division process. In restoring division, each quotient digit has one of the values 0,1, . . . , r -1, for an arbitrary integer radix r. In nonrestoring division, each quotient digit has one of the values -(r-1),. . ., -1, +1, . . ., +(r-1). For the division methods described here, each quotient digit has one of the values -n, -(n-1), . . ., -1, 0, 1, . . . n-1, n, where n is an integer such that ½(r-1)≤n≤r-1. A method for serial conversion of the quotient digits to conventional (restoring) form is given. Examples of new division procedures for radix 4 and radix 10 are given.