From http://knol.google.com/k/counting-in-binary-for-beginners#
Take the decimal number 11,111 - Here's what the "1" in each column means in decimal, where each column represents various sets of "ten's"
Decimal | "10,000's" (104) | "1000's" (10x10x10, or 103) | "100's" (10x10, or 102) | "10's" | "1's" | |
1 | 1 | 1 | 1 | 1 |
So one group of 10,000,
plus one group of 1,000,
plus one group of 100,
plus one group of 10,
plus 1,
Or more commonly, 11,111.
Let's look at the same number - 11111 - in binary, where each column represents sets of "two's"
Binary | "16's" (24) | "8's" (2x2x2, or 23) | "4's" (2x2, or 22) | "2's" | "1's" |
1 | 1 | 1 | 1 | 1 |
So one group of 16,
plus one group of 8,
plus one group of 4,
plus one group of 2,
plus 1,
Comes out, in numbers most of us would understand, as (16+8+4+2+1) = 31.
So 11111 in binary = 31 in decimal
thanks http://knol.google.com/k/counting-in-binary-for-beginners#
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