Binary System: 두 판 사이의 차이
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2007년 11월 7일 (수) 20:32 기준 최신판
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Because binary uses base two as opposed to the decimal base ten, the numbers get larger much more quickly, but they still obey the same principles. In this case, the number ten is represented by 10 (no 1s, one x 10) in decimal, and 1010 (no 1s, one x 2, no 4s, one x 8) in binary. |
Conversion
To convert a decimal number to binary, you need only keep subtracting the largest power of two. Here the decimal 200 is represented by 11001000 (one x 128, one x 64, no 32s, no 16s, one x 8, no 4s, no 2s, no 1s)
From binary to decimal is even easier - just add up the columns.
100 | 10 | 1 |
2 | 0 | 0 |
2 x 100 + 0 + 0 = 200 |
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 x 128 + 1 x 64 + 0 + 0 + 1 x 8 + 0 + 0 + 0 =200 |
Addition
Again, addition differs only from decimal in that it is using base two.
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The only trick here is to remember that it is base 2 - whereas in decimal 1 + 1 = 2 with nothing to carry into the next column, in binary, 1 + 1 still = 2, but that 2 is carried forward (as a 1, naturally).
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