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Never really thought about it until recently, but it looks like the number 111 appears very frequently in clock speeds and such: the first example that comes to my mind is one of the handheld game consoles that came with 333mhz CPU (usually downclocked to 222 for battery life), and RAMs also sometimes come with clock speed that are multiples, or at least close to that of 111 (333 for PC2700, 2,666 for DDR4 2666.)

To me, the numbers that are powers of 2 seems very logical, but 111 really looks like it just came out of nowhere but I can still find them rather often. Is it just a pure coincidence, or is there any historical or mathematical background to it?

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It's not 111, it's small integer fractions. 1000/3 = 333 MHz, 5000/3 = 1666, etc. Small integer fractions are easier to implement in PLLs for clock generation. If you start with a reference of, say, 100 MHz, then you can get to all of these values with small integer divider values.

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My opinion as a designer is that people, espe marketing types, like nice memorable numbers. I rather doubt that a 333MHz processor really runs at 333MHz. More likely a little bit off from that, but rounded up or down to a neat number.

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    \$\begingroup\$ Intel in particular iterated lots of their frequencies in 33MHz steps. The next generation going 33MHz faster than the previous etc. The CPU did execute at that exact clock speed. If they picked 33MHz steps for technical, marketing or other reasons, I have no idea. \$\endgroup\$ – Lundin Jun 27 at 11:00

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