A single-chip multiprocessor (2, 102) is disclosed. The multiprocessor (2, 102) includes multiple central processing units, or CPUs, (10, 110) that share a floating-point unit (5, 105). The floating-point unit (5, 105) may receive floating-point instruction codes from either or both of the multiple CPUs (10, 110) in the multiprocessor (2, 102), and includes circuitry (52) for decoding the floating-point instructions for execution by its execution circuitry (65). A dispatch unit (56) in the floating-point unit (5, 105) performs arbitration between floating-point instructions if more than one of the CPUs (10, 110) is forwarding instructions to the floating-point unit (5, 105) at the same time. Dedicated register banks, preferably in the form of stacks (60), are provided in the floating-point unit (5, 105). The disclosed multiprocessor (2, 102) provides efficiency in allowing sharing of the floating-point unit (5, 105) by the multiple CPUs (10, 110), considering that the utilization of a floating-point unit (5,105) by a single CPU (10, 110) is generally relatively low.