A Time-Efficient CMOS-Memristive Programmable Circuit Realizing Logic Functions in Generalized AND–XOR Structures

This paper describes a CMOS-memristive programmable logic device connected to CMOS XOR gates (mPLD-XOR) for realizing multioutput functions well suited for two-level {NAND, AND, NOR, OR}-XOR-based design. This structure is a generalized form of AND–XOR logic where any combination of NAND, AND, NOR, and OR, and literals can replace the and level. For mPLD-XOR, the computational delay, which is measured as the number of clock cycles, equals the maximum number of inputs to any output XOR gate of a function assuming that the number of XOR gates is large enough to calculate the outputs of the function simultaneously. The input levels of functions are implemented with novel programmable diode gates, which rely on the diode-like behavior of self-rectifying memristors, and the output levels of functions are realized with CMOS modulo-two counters. As an example, the circuit implementation of a 3-bit adder and a 3-bit multiplier are presented. The size and performance of the implemented circuits are estimated and compared with those of the equivalent circuits realized with stateful logic gates. Adding a feedback circuit to the mPLD-XOR allows the implementation of a multilevel XOR logic network with any combination of sums, products, XORs, and literals at the input of any XOR gate. The mPLD-XOR with feedback can reduce the size and number of computational steps (clock cycles) in realizing logic functions, which makes it well suited for use in communication and parallel computing systems where fast arithmetic operations are demanding.