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2 to the 10th is approximately equal to 10 to the 3rd

 
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brian-hansen
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Joined: 17 Mar 2006
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Location: Oregon

PostPosted: Sun May 14, 2006 2:22 am    Post subject: 2 to the 10th is approximately equal to 10 to the 3rd Reply with quote

I suppose every computer science graduate knows this one well, but when I taught computer science undergrads, many did not.

This is a phenomenally useful conversion, that allows us to make human sense of binary numbers.

Contrary to the opinions of IT recruiters and Y2K pundits, a "K" is not equal to 1000, but is equal to 1024, or 2 to the 10th power. By this measurement, we have not yet reached Y2K, and won't for 42 more years!

-Brian
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brian-hansen
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PostPosted: Mon Feb 04, 2013 6:05 pm    Post subject: Reply with quote

Perhaps it is worth adding a few related ideas. First, these factors apply well to larger quantities, so:

2 to the 20 == 2 to the (10 + 10) == (2 to the 10) * (2 to the 10)
This is approx. (10 to the 3) * (10 to the 3) == 10 to the 6 == 1 million.

32 bits is 2 squared * 2 to the 30
== (approx) 4 * 10 to the 9 == 4,000,000,000 == 4 billion

[As an illustration, 32 bits is not enough to represent each individual in the world with their own unique id.]


Also to smaller quantities:

If you know something is 1 in a million, then the chances are 10 to the -6. In binary, the rough equivalent would be 2 to the -20.
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