Embodiments of the present invention provide a hardware accelerator that assists a host database system in processing its queries. The hardware accelerator comprises special purpose processing elements that are capable of receiving database query/operation tasks in the form of machine code database instructions, execute them in hardware without software, and return the query/operation result back to the host system. For example, table and column descriptors are embedded in the machine code database instructions. For ease of installation, the hardware accelerators employ a standard interconnect, such as a PCle or HT interconnect. The processing elements implement a novel dataflow design and Inter Macro-Op Communication (IMC) data structures to execute the machine code database instructions. The hardware accelerator may also comprise a relatively large memory to enhance the hardware execution of the query/operation tasks requested. The hardware accelerator utilizes hardware-friendly memory addressing, which allows for arithmetic derivation of a physical address from a global database virtual address simply based on a row identifier. The hardware accelerator minimizes memory reads/writes by keeping most intermediate results flowing through IMCs in pipelined and parallel fashion. Furthermore, the hardware accelerator may employ task pipelining and pre-fetch pipelining to enhance its performance.