A data ALU (arithmetic logic unit) (54) in a data processing system (20) performs both 24-bit arithmetic, and 16-bit exact arithmetic (including shifting and logical operations) using the same hardware. For a multiply/accumulate operation in 16-bit exact mode, shifting operations are used to align the operands so that 16-bit exact mode is transparent to a user. An entire instruction set can be executed in 24-bit mode or 16-bit exact mode. The same instructions and hardware are used in both modes. A transition between modes is performed by changing a status bit (97) in a status register (95).