Logic synthesis and a generalized notation for memristor-realized material implication gates

Abstract

The paper presents new logic synthesis methods for single-output incomplete multi-level binary circuits using Memristor-based material implication gates. The first method follows Lehtonen's assumption of using only two working memristors. The algorithm minimizes the number of implication (IMPLY) gates, which corresponds to minimizing the number of pulses or the delay time. This greedy search method uses essential and secondary essential primes, does not require solving the covering problem, is fast, and produces high quality results. We compare it to other synthesis methods, such as the modified SOP and Exclusive-Or Sum of Products (ESOP) with minimum number of working memristors. We analyze the problem of reduction in IMPLY gate count by adding more working memristors and introduce Imply Sequence Diagrams, a new notation, similar to one used in reversible logic.

Devising a method of figurative transformations for minimizing boolean functions in the implicative basis

“…New methods of logical synthesis for incomplete multilevel binary chains using memristor-based implication elements are considered in work [12]. The first method checks the assumption of the use of only two working memristors.…”

“…The literary sources considered above [4][5][6][7][8][9][10][11][12][13] represent the implementation of the fourth basic element of scheme equipment -the memristor, which is an addition to the resistor, capacitor, and inductiveness.…”

Memristor-Based Volistor Gates Compute Logic with Low Power Consumption

“…In theory [10][11] every single-output Boolean function of n variables can be realized in a crosspoint array with n source memristors and two additional working memristors. These working memristors can act as both source and target memristors.…”

Efficient Algorithms for In-Memory Fixed Point Multiplication Using MAGIC

“…Since data is stored in RRAM as resistance, information can be stored and processed using the same cells, with no need for conversion, sensing or moving of data. These advantages have been the driving force behind many recent works on MAGIC and similar techniques [16]- [20]. An important feature of MAGIC is that when the inputs and outputs of different gates are located in the same row/column, the operation of all gates can be executed simultaneously in a single cycle.…”