\(0.65_8 = 0 + 6 \times 8^{-1} + 5 \times 8^{-2}\)
= 0 + \(\frac{6}{8} + \frac{5}{64}\) = 0.828125 base 10
0.828125 base 10 to base 2
| 0.828125 X 2 = 1.65625 | 1 |
| 0.65625 X 2 = 1.3125 | 1 |
| 0.3125 X 2 = 0.625 | 0 |
| 0.625 X 2 = 1.25 | 1 |
| 0.25 X 2 = 0.5 | 0 |
| 0.5 X 2 = 1.0 | 1 |
read answer from up to down
0.828125 in base 10 = 0.110101 in base 2.
Therefore, 0.65 in base 8 = 0.110101 in base 2.
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