A computer system and method for operating a computer system capable of running in mutually incompatible real and protected addressing modes, in which programs written for one mode can be run in the other mode without modification. The operating system using BIOS assembles two different common data areas for the two modes, each inclusive of device block pointers, function transfer table pointers, data pointers, and function pointers. The common data area for the real mode is assembled first. To assemble the pointers for the protected mode common data area, the offset values from the real mode area are copied directly, and then selector values are inserted whose physical addresses correspond to the segments of the corresponding pointers in the real mode area. The selector values are derived from a segment descriptor table.