Question 1143404
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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.<br>
Here are alternatives for the methods for doing both conversions, without using the place values in base 5 and base 2.<br>
(1) Converting 134 base 5 to base 10.<br>
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<br>
(2) Converting 44 base 10 to base 2.<br>
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