We report recent progress in the development of rapid single-flux-quantum (RSFQ) microprocessors integrated with random access memories (RAMs) based on bit-serial processing, called CORE e series. The bit-serial processing is an efficient, unique approach for RSFQ microprocessors that target ultrafast clock frequency with small hardware size. The CORE e series have a richer instruction set and RAMs integrated on the same die, and are capable of running small-scale benchmark programs. We are currently developing three microprocessors in parallel, CORE e2, e3, and e4, for different purposes including prototype demonstration, investigation on efficient use of hardware and energy, and full-function implementation. Here we describe design and implementation of the CORE e microprocessors together with a high-density shift-register-based RAM. The estimated performance of these microprocessors is 333 million instructions per second (MIPS) with 4.6-5.6 mW power.