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\n" ); document.write( "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.
\n" ); document.write( "Here are alternatives for the methods for doing both conversions, without using the place values in base 5 and base 2.
\n" ); document.write( "(1) Converting 134 base 5 to base 10.
\n" ); document.write( "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:
\n" ); document.write( "1*5 = 5; 5+3 = 8
\n" ); document.write( "8*5 = 40; 40+4 = 44
\n" ); document.write( "134 base 5 = 44 base 10
\n" ); document.write( "(2) Converting 44 base 10 to base 2.
\n" ); document.write( "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:
\n" ); document.write( "44/2 = 22 remainder 0
\n" ); document.write( "22/2 = 11 remainder 0
\n" ); document.write( "11/2 = 5 remainder 1
\n" ); document.write( "5/2 = 2 remainder 1
\n" ); document.write( "2/2 = 1 remainder 0
\n" ); document.write( "1/2 = 0 remainder 1
\n" ); document.write( "44 base 10 = 101100 base 2 \n" ); document.write( "