A Minimum Table Size Result for Higher Radix Nonrestoring Division

The minimum table size is established for nonrestoring division algorithms that utilize a table lookup technique for quotient digit selection. It is assumed that the dividend and divisor are n-bit fractions, that the algorithm is radix 2
^q
, q ≥ 2, and that the algorithm uses the table on an iteration in which any remainder in the range 0 to 1/2 – 1/2
ⁿ⁺¹
can occur as, for example, in the first iteration. In addition, it is shown how to construct tables that apply to both positive and negative remainders where negative remainders are represented in 2's complement mode.