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Are memory to memory instructions allowed?

Eg. ADD [123], [345] or MOV [123], [343]

If not, then why?

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In RISC instructions set  all operands involved in an arithmetic or logic operation must either be in processor registers, or one of the operands may be given explicitly within the instruction word.

and memory operands are accessed only using load store instructions.  

                                                        -Hamacher

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