The present invention provides a data processor or a data processing system which can be used in compatible modes among which the number of bits of an address specifying a logical address space varies at the time of referring to a branch address table by extension of displacement of a branch instruction. At the time of generating a branch address of a first branch instruction, the data processor or the data processing system optimizes a multiple with which a displacement is multiplied in accordance with the number of bits of an address specifying a logical address space, adds extended address information to the value of a register, and refers to a branch address table with address information obtained by the addition. The referred information is used as a branch address. To be adapted to a compatible mode using different number of bits of an address specifying a logical address space, it is sufficient to change a multiple with which the displacement is multiplied in accordance with the mode.