First lets prove that 758 & 1111012 are really equal to 6110.
758 = 5x80+ 7x81
=5x1 + 7x8
=5 + 56
=6110
1111012 = 1x20 + 0x21 + 1x22 + 1x23 + 1x24 + 1x25
= 1x1 | + 0x2 | + 1x4 | + 1x8 | + 1x16 | + 1x32 |
= 1 | + 0 | + 4 | + 8 | + 16 | + 32 |
= 6110 |
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Notice that if we take the base 8 number of 75 and convert each
digit to base 2, we have the same number as when we converted the base 10
number to base 2. i.e.
Convert 7 to base 2
2
2
2
3 | R=1 |
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7 |
| |
1 | R=1 |
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3 |
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0 | R=1 | 1112 |
1 |
2
2
2
| Convert 5 to base 2 | |
2 | R=1 |
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5 |
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1 | R=0 |
|
2 |
| |
0 | R=1 | 1012 |
1 | ||
