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There is a shortcut when converting from one base to another base (such as base 6 to base 10). You can multiply: |
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4 * 216 = 864
2 * 36 = 72
5 * 6 = 30
2 * 1 = 2
Total 968 |
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Base 2 is the ultimate extension of this idea. There are only two digits: 0 and 1. The columns are |
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To convert the number 88 to base 2, you follow the same procedure: There are no 128s, so column 8 is 0. There is one 64 in 88, so column 7 is 1 and 24 is the remainder. There are no 32s in 24, so column 6 is 0. There is one 16 in 24, so column 5 is 1. The remainder is 8. There is one 8 in 8, and so column 4 is 1. There is no remainder, so the rest of the columns are 0. |
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To test this answer, convert it back: |
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1 * 64 = 64
0 * 32 = 0
1 * 16 = 16
1 * 8 = 8
0 * 4 = 0
0 * 2 = 0
0 * 1 = 0
Total 88
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The power of base 2 is that it corresponds so cleanly to what a computer needs to represent. Computers do not really know anything at all about letters, numerals, instructions, or programs. At their core they are just circuitry, and at a given juncture there either is a lot of power or there is very little. |
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To keep the logic clean, engineers do not treat this as a relative scale (a little power, some power, more power, lots of power, tons of power), but rather as a binary scale (enough |
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