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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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Memory to Memory operations aren't allowed in RISC architecture because it takes significant time for accessing the Main memory(CISC allows it).. while in RISC we only deal with registers while doing arithmetic operations like ADD,SUB etc.. Only during LOAD and STORE MM is accessed..
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I think RISC architectures wont allow such instructions but CISC may allow such instructions.
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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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