OS: Hyper threading ?

Question

I am confused with all 32/64 bit architecture for Hardware/OS/Binary, Can someone please help in clarifying this queries?

1. Of'course 64 bit hardware is faster than 32 bit, still there are people who prefer 32 bit over 64 bit hardware, Why so?
2. If I have 32 bit Hardware then On that can I run 64 bit OS? (and vice versa)
3. If I have a 64 bit Hardware and 32 bit OS then what will be the speed of my OS, as per 32 bit or as per 64 bit? (and vice versa)
4. If I have 32 bit OS then can I run binary of 64 bit on that? (and vice versa)
5. Is it necessary to compile binary with 32/64 bit both or we can compile with any and use it in both?
6. Is the speed of the process also depends on type of binary that I have? For example, If I have 64 bit hardware and 64 bit OS but I have a binary which is compiled with 32 bit compiler then what will be the speed difference?

P.S. I know its basic and silly queries but lets clear now before it gets too late. :)

Answer 1

Hyper-threading works by duplicating certain sections of the processor—those that store the architectural state—but not duplicating the main execution resources. This allows a hyper-threading processor to appear as two "logical" processors to the host operating system, allowing the operating system to schedule two threads or processes simultaneously. When execution resources would not be used by the current task in a processor without hyper-threading, and especially when the processor is stalled, a hyper-threading equipped processor can use those execution resources to execute another scheduled task.