We "naturalize" the handshake communication links of a self-timed system by assigning the capabilities of filling and draining a link and of storing its full or empty status to the link itself. This contrasts with assigning these capabilities to the joints, the modules connected by the links, as was previously done. Under naturalized communication, the differences between Micropipeline, GasP, Mousetrap, and Click circuits are seen only in the links -the joints become identical; past, present, and future link and joint designs become interchangeable.We also "naturalize" the actions of a self-timed system, giving actions status equal to states -for the purpose of silicon test and debug. We partner traditional scan test techniques dedicated to state with new test capabilities dedicated to action. To each and every joint, we add a novel proper-start-stop circuit, called MrGO, that permits or forbids the action of that joint. MrGO, pronounced "Mister GO," makes it possible to (1) exit an initial state cleanly to start circuit operation in a delay-insensitive manner, (2) stop a running circuit in a clean and delay-insensitive manner, (3) single-or multi-step circuit operations for test and debug, and (4) test sub-systems at speed.
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 signeddigit 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% in latency per iteration over a standard radix-2 SRT algorithm at the cost of 36% more power and 50% more area.
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