Is it possible to construct a secure operating system for these computer systems which not provide a privileged mode of operation in hardware?

Yes, it is possible to construct a secure operating system for hardware that does not provide a privileged mode of operation, although it presents significant challenges. Such systems can implement security through techniques like software-based isolation, sandboxing, and capability-based security models, which help manage access rights and protect processes from each other. However, without hardware support for privilege levels, the OS must rely heavily on rigorous software controls and may be more vulnerable to certain types of attacks compared to systems with hardware-enforced privilege. Overall, while feasible, achieving a high level of security in such environments is complex and requires careful design and implementation.