Question 671116: what is 346 in base 8 minus 405 in base 8?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! good question.
what is 346 in base 8 minus 405 in base 8.
assuming these numbers are already in base 8, then you would subtract 346 from 405 and then give the answer the negative sign because the number you are subtracting is larger than the number you are subtracting from.
you would get:
346 - 405 is equal to - (405 - 346)
you would try to subtract the 6 from the 5 which you can't do because the 6 is larger than the 5.
you need to borrow from the next position.
since the next digit over is 0, you need to go over 1 more digit and borrow from the 4.
the 4 becomes 3.
the 0 becomes 8 (remember you're in base of 8 not base of 10).
now you can borrow from the second digit, so the second digit becomes 7 and the first digit becomes 5 + 8 = 13
you can now subtract 6 from 13 to get 7 for the first digit
you can now subtract 4 from 7 to get 3 for the second digit.
you can now subtract 3 from 3 to get 0 for the first digit.
the answer should be -37 in the base of 8.
a good way to check is to convert everything to base of 10, perform the operation, and then convert everything back to the base of 8.
to convert 405 from the base of 8 to the base of 10, do the following:
4 * 8^2 + 0 * 8^1 + 5 * 8^0 = 261
405 in the base of 8 is equivalent to 261 in the base of 10.
to convert 346 from the base of 8 to the base of 10, do the following:
3 * 8^2 + 4 * 8^1 + 6 * 8^0 = 192 + 32 + 6 = 230.
346 in the base of 8 is equivalent to 230 in the base of 10.
now subtract 261 from 230 to get an answer of -31 in the base of 10.
now convert -31 from the base of 10 to the base of 8.
the way to convert from the base of 10 to the base of 8 is to repeatedly divide the number by 8 and then use the remainders in reverse order from how they were created.
as an example, since we already know that 405 in the base of 8 is equal to 261 in the base of 10, we will convert 261 from the base of 10 to the equivalent number in the base of 8.
if we get 405 then we know we did it right.
261 divided by 8 = 32 with a remainder of 5
32 / 8 = 4 with a remainder of 0
4 / 8 = 0 with a remainder of 4
going with the remainders in reverse order of ho they were created, you get 405 which is the the number 261 in base 8 format.
i'll convert 230 in the base of 10 to its equivalent number in the base of 8.
if i get 346, then i did it right.
230 / 8 = 28 with a remainder of 6
28 / 8 = 3 with a remainder of 4
3 / 8 = 0 with a remainder of 3
gathering my remainders in the reverse order from which they created, i get 346 as the equivalent number in the base of 8.
since this agrees with what i already knew, then i did it correctly.
now back to the original problem.
in base of 10, the difference was -31
convert this to octal format as follows:
31 / 8 = 3 with a remainder of 7
3 / 8 = 0 with a remainder of 3
the number in octal format is -37.
this agrees with the arithmetic up front so we're good.
i got the same answer both ways.
way 1 was performing the arithmetic directly in the base of 8.
way 2 was converting everything to the base of 10 and performing the arithmetic and then converting the answer back to the base of 8.
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