SOLUTION: evaluate 134 base5 to base2

Question 1143404: evaluate 134 base5 to base2

Found 2 solutions by math_helper, greenestamps:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
I find it easiest to first convert to base 10 then over to the final base:
134 (base 5) = = 44 (base 10)

44 (base 10) = = 101100 (base 2)

Started at because
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

I agree that converting from base 5 to base 10 and then from base 10 to base 2 is easiest, although the conversion can be done directly.

Here are alternatives for the methods for doing both conversions, without using the place values in base 5 and base 2.

(1) Converting 134 base 5 to base 10.

The method is to start with the leftmost digit and repeatedly multiply by the base and add the next digit, until all digits have been used:
1*5 = 5; 5+3 = 8
8*5 = 40; 40+4 = 44
134 base 5 = 44 base 10

(2) Converting 44 base 10 to base 2.

The method is to repeatedly divide by the new base, 2, noting the remainders each time. Those remainders are the base 2 digits, starting with the rightmost digit:
44/2 = 22 remainder 0
22/2 = 11 remainder 0
11/2 = 5 remainder 1
5/2 = 2 remainder 1
2/2 = 1 remainder 0
1/2 = 0 remainder 1
44 base 10 = 101100 base 2
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