Yup everything is pretty much the same, other than pre-386 chips only had the AX (16) type registers while everyhting after had EAX (32)
If you are using a 16 bit assembler, you can still use 32 bit registers
DB 66H
MOV AX,[esi+1]
will make a 16 bit assemblers do...
MOV EAX,[ESI+1]
This works in almost all cases where you are trying to make the destination 32 bit
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Even if your using an old assebmler, you can even manually enter SIMD instructions, though i do not know those off the top of my head.
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Hammer will be the first x86 cpu to really add to the register set since the 386. Whats unclear at the moment is if it will or will not allow a form of 66H override, I have seen refereance to a 69H override in x86-64 that claims to force an operation to 64 bit. but occording to the published docs, you must be in 64bit protected mode to do this, it could be as simple as telling the CPU to do this, or it could be as complicated as trying to enter protected mode manually was from 16 bit mode.
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Have fun, it's really fun to hand code things in sometimes just to show off.