Parallel hierarchical memory (PI memory) is a new type of memory that is designed to improve the performance of parallel computing systems. PI memory is composed of two blocks: a mask RAM and a tail element RAM. The mask RAM stores the masks that are used to encode the information, while the tail element RAM stores the actual information. The address block of the PI memory is responsible for generating the physical addresses of the cells where the tail elements and their masks are stored. The address block also stores the field of addresses where the array was written and associates this field of addresses with the corresponding external address used to write the array. The proposed address block structure is able to efficiently generate the physical addresses of the cells where the tail elements and their masks are stored. The address block is also able to store the field of addresses where the array was written and associate this field of addresses with the corresponding external address used to write the array. The proposed address block structure has been implemented in a prototype PI memory. The prototype PI memory has been shown to be able to achieve significant performance improvements over traditional memory architectures. The paper will present a detailed description of the PI transformation algorithm, a description of the different modes of addressing organization that can be used in PI memory, an analysis of the efficiency of parallel-hierarchical memory structures, and a discussion of the challenges and future research directions in the field of PI memory.