1. A parallel data processing system comprising: a plurality of data processing units; a plurality of trays, each including only one register, for storing and transmitting data, each of said plurality of trays being connected to each of said plurality of data processing units in only a one-to-one correspondence and being connected to each other only one-dimensionally through a data transmission path; a plurality of tray connection switching means for selectively changing a connection of said plurality of trays via said data transmission path to either a first connection state or a second connection state, for dividing said plurality of trays and said plurality of data processing units each into a plurality of groups, and for permitting each of said plurality of groups to perform an independent operation, said first connection state having a first number of said plurality of groups of said trays connected via said data transmission path and said second connection state having a second number of said plurality of groups of said trays connected via said data transmission path, said second number being larger than said first number; and a clock generating unit for generating a clock signal for synchronizing a data transmitting operation between said plurality of trays through said data transmission path and a data processing operation performed by said plurality of data processing units.