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Since the CPU runs in user/kernel mode, I want to know how this is determined by kernel. I mean, if a sys call is invoked, the kernel executes it on behalf of the process, but how does the kernel know that it is executing in kernel mode?
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The system is in user mode when the operating system is running a user application such as handling a text editor. The transition from user mode to kernel mode occurs when the application requests the help of operating system or an interrupt or a system call occurs. The mode bit is set to 1 in the user mode.
In kernel mode, the program has direct and unrestricted access to system resources. In user mode, the application program executes and starts. In user mode, a single process fails if an interrupt occurs. Kernel mode is also known as the master mode, privileged mode, or system mode.
In modern operating systems, applications are separated from the operating system itself. The operating system code runs in a privileged processor mode known as kernel mode and has access to system data and hardware.
A full kernel controls all hardware resources (e.g. I/O, memory, cryptography) via device drivers, arbitrates conflicts between processes concerning such resources, and optimizes the utilization of common resources e.g. CPU & cache usage, file systems, and network sockets.
You can tell if you're in user-mode or kernel-mode from the privilege level set in the code-segment register (CS). Every instruction loaded into the CPU from the memory pointed to by the RIP or EIP register (the instruction pointer register depending on if you are x86_64 or x86 respectively) will read from the segment described in the global descriptor table (GDT) by the current code-segment descriptor. The lower two-bits of the code segment descriptor will determine the current privilege level that the code is executing at. When a syscall is made, which is typically done through a software interrupt, the CPU will check the current privilege-level, and if it's in user-mode, will exchange the current code-segment descriptor for a kernel-level one as determined by the syscall's software interrupt gate descriptor, as well as make a stack-switch and save the current flags, the user-level CS value and RIP value on this new kernel-level stack. When the syscall is complete, the user-mode CS value, flags, and instruction pointer (EIP or RIP) value are restored from the kernel-stack, and a stack-switch is made back to the current executing processes' stack.
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