Using Memristor Technology for Multi-value Registers in Signed-digit Arithmetic Circuits

Signed-digit (SD) arithmetic exploits positive and negative digits requiring more than two states. It is long known that an addition using trits, i.e. each digit stores not only a 0 or a 1 but also either 2 or -1, requires only a constant number of steps independent of the operands' word length. However, current processors could not profit from that due to the lack of fast, dense and CMOS compatible memory cells that can store reliably multiple states. Memristors offer these features making it necessary to re-evaluate different SD number representations and to evaluate the consequences of an implementation of a multi-value register file with memristors concerning latency, area and energy consumption. Using memristors as multi-value register reduces latency and area on one side compared to flip-flop based memories. On the other side this requires additional sophisticated control circuitry to implement ADCs/DACs, current limiting circuits and to generate control signals to read, write and erase memristors. The paper determines the break-even points at which ternary circuits attached to memristor based registers show better energy-delay products and less area consumption and how much power consumption these improvements cost. By layout synthesis is shown that ternary adders with trit-storing memristors can reduce the latency for a word length of 16 digits about 19% and about 52% for 512 digits compared to a binary carry-look-ahead (CLA) adder with nearly the same power consumption.