Hardware input/output address translation apparatus adapted for use in a multitasking computer system including hardware responsive to commands from an unprivileged application program addressed to an input/output address for translating the input/output address to a physical address space of an input/output device and transferring the command to the physical address of an input/output device, and additional hardware responsive to commands from an unprivileged application program addressed to an input/output address for selecting from safe translations of input/output addresses to physical address spaces of input/output devices for the hardware for translating the input/output address to a physical address space of an input/output device.