  Redox-based resistive switching devices (ReRAM) are an emerging class of
non-volatile storage elements suited for nanoscale memory applications. In
terms of logic operations, ReRAM devices were suggested to be used as
programmable interconnects, large-scale look-up tables or for sequential logic
operations. However, without additional selector devices these approaches are
not suited for use in large scale nanocrossbar memory arrays, which is the
preferred architecture for ReRAM devices due to the minimum area consumption.
To overcome this issue for the sequential logic approach, we recently
introduced a novel concept, which is suited for passive crossbar arrays using
complementary resistive switches (CRSs). CRS cells offer two high resistive
storage states, and thus, parasitic sneak currents are efficiently avoided.
However, until now the CRS-based logic-in-memory approach was only shown to be
able to perform basic Boolean logic operations using a single CRS cell. In this
paper, we introduce two multi-bit adder schemes using the CRS-based
logic-in-memory approach. We proof the concepts by means of SPICE simulations
using a dynamical memristive device model of a ReRAM cell. Finally, we show the
advantages of our novel adder concept in terms of step count and number of
devices in comparison to a recently published adder approach, which applies the
conventional ReRAM-based sequential logic concept introduced by Borghetti et
al.
