This paper deals with an efficient radix-2 divider design theory that uses carry-propagation-free adders based on redundant binary{1, 0, 1} representation. In order to compute the division fast, we look ahead to the next step quotient-digit selection embedded in the current partial remainder calculation. The solution is a function of the four most significant digits of the current partial remainder, when scaling the divisor in the range [1, 9/8). In gate depth, this result is better than the higher radix-4 case without the look-ahead quotient-digit selection and the design is simple.

This paper deals with the theory and design method of an efficient radix-4 divider using carry-propagation-free adders based on redundant binary {-1,0,+1} representation. The usual method of normalizing the divisor in the range [1/2,1) eliminates the advantages of using a higher radix than two, bacause many digits of the partial remainder are required to select the quotient digits. In the radix-4 case, it is shown that it is possible to select the quotient digits to refer to only the four (in the usual normalizing method it is seven) most significant digits of the partial remainder, by scaling the divisor in the range [12/8,13/8). This leads to radix-4 dividers more effective than radix-2 ones. We use the hyperstring graph representation proposed in Ref.(18) for redundant binary adders.