Radix-2 Division Algorithms with an Over-Redundant Digit Set

This paper presents a derivation of four radix-2 division algorithms by digit recurrence. Each division algorithm selects a quotient digit from the over-redundant digit set {-2, -1, 0, 1, 2}, and the selection of each quotient digit depends only on the two most-significant digits of the partial remainder in a redundant representation. Two algorithms use a two´s complement representation for the partial remainder and carry-save additions, and the other two algorithms use a binary signed-digit representation for the partial remainder and carry-free additions. Three algorithms are novel. The fourth algorithm has been presented before. Results from the synthesized netlists show that two of our fastest algorithms achieve an improvement of 10 percent in latency per iteration over a standard radix-2 SRT algorithm at the cost of 36 percent more power and 50 percent more area.