In an aspect, a processor supports modeless execution of 64 bit and 32 bit instructions. A Load/Store Unit (LSU) decodes an instruction that without explicit opcode data indicating whether the instruction is to operate in a 32 or 64 bit memory address space. LSU treats the instruction either as a 32 or 64 bit instruction in dependence on values in an upper 32 bits of one or more 64 bit operands supplied to create an effective address in memory. In an example, a 4 GB space addressed by 32-bit memory space is divided between upper and lower portions of a 64-bit address space, such that a 32-bit instruction is differentiated from a 64-bit instruction in dependence on whether an upper 32 bits of one or more operands is either all binary 1 or all binary 0. Such a processor may support decoding of different arithmetic instructions for 32-bit and 64-bit operations.