There’s a difference between “faster” and “more powerful”. I’ll address “faster”.
The key thing in being faster is of course the clock speed. The internal clock of a microprocessor synchronizes most of the processing within the chip, kind of like marchers moving along to the beat of a drum. Faster beat, faster marching.
But there’s at least one other aspect of “faster”, which borders on “more powerful”. That is how many clock ticks it takes to do a given operation. If processor A is clocked at 2 GHz and takes 4 clock cycles to execute a floating point multiply, and processor B is clocked at 1 GHz and takes 1 clock cycle to do a FP multiply, processor B is faster (at doing that particular thing) even though A is clocked at a higher rate of speed.
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