In the post Moore era, post-CMOS technologies have received intense interests for possible future digital logic applications beyond the CMOS scaling limits. In the meantime, from the system perspective, non-von-Neumann architectures such as processing-in-memory (PIM) are extensively explored to overcome the bottleneck of modern computers, known as the memory wall, for high-performance energy-efficient integrated circuits. In this paper, we propose functionally complete nonvolatile logic gates based on a 2-transistor-2-RRAM (2T2R) unit structure, which is then used to form a reconfigurable 3transistor-2-RRAM (3T2R) chain with programmable interconnects for complex combinational logic circuits, and a dense 3-dimensional (3-D) stacked memory array architecture. The design has a highly regular and symmetric structure, while operations are flexible yet simple, without the need of complicated peripheral circuitry or a third resistive state. Implementations of XNOR gate and full-adder using 3T2R chain without extra routing/control gates or resistors are shown as demonstration examples of arithmetic unit design. The proposed computing scheme is intrinsic, efficient with superior performance in speed and area. Easily integrated as 3-D stacked array, the proposed memory architecture not only serves as regular 3-D memory array but also performs logic computation within the same layer and between the stacked layers. Concurrent computations under multiple computation modes for flexible operations in the memory are presented. Bias schemes for selected/half-selected/unselected cells are also explained and verified.