How』d you convert 567₁₀
from base 10 to base 8?
Firstly, we』ll see the largest power of 8 that is smaller or equals to 567. We found that 8³ = 512 is it.
Next, we see how many 512’s are there in 567, and there’s only 1.
So, the first digit (leftmost digit) is going to be 1 (meaning 1× 8³), and we have 567-512 = 55 left.
Next, we check what we』ll have for the next digit to the right, the 8² = 64 digit. Since 55 < 64, we won’t have any digit for that, so the second digit is 0.
We then check for the third digit, which is the 8¹ digit. 55 = 6 × 8 + 7, so we』ll have 6 for this digit.
We now have 55 – 48 = 7 left.
We then check for the fourth digit, the 1 digit. This is just the 7 that is left.
So overall, 567₁₀= 1067₈.
After we know this,
similar computations can be applied to all number systems to transfer them back and forth. Notice how the time system we use is actually base 60, where 60 seconds will become 1 minute and 60 minutes will become 1 hour. So, 1 hour 1 minute 1 second doesn’t mean 111 seconds;
instead it means
111₆₀ = 3600 + 60 + 1 = 3661₁₀ seconds.