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simulation and modeling is an another issue for me.
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To simulate a system using another system you need to model it first.
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"You can also produce another hardware platform to directly model your hardware and this is emulation without using software."
Is that mean FPGA(or any programmable logic)? can you give some example.
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fpga prototyping for asic target is a type of emulation(though commercial emulators add extra debug features, not just fpga). Using a cyclone device to test a program meant for stratix is also emulation.
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"If you are modelling software itself with another software then this can be viewed as emulation as well."
What do you mean by modeling software itself?
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in fact the word emulation was first coined for software.
Example, you design FIR filter and model in your PC. If your final target is a DSP(software) based FIR then you are emulating it on the PC(if we ignore the difference of instruction sets between PC and DSP). If your target is FPGA then you are simulating it.
Don't worry much about terms, they are context dependant, relative and may vary. All you need is to know first we have two systems, one used to copy the other. Simulation models a system(e.g. your fpga) using a different system(PC software). Emulation models like by like(as close as possible, possibly never exactly).