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A 3.2 GHz processor can theoretically execute up to 3.2 billion cycles per second. The number of instructions processed per cycle varies based on the architecture and design of the processor, typically ranging from 1 to 4 instructions per cycle for modern CPUs. Therefore, if we assume an average of 2 instructions per cycle, the maximum instructions processed in one second would be around 6.4 billion. However, actual performance can be lower due to factors like instruction dependencies and other bottlenecks.

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