# College Math 213

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write each of the following in the indicated base.
1011two to base ten
1574 to base twelve
MCMLIV to base ten

• College Math 213 -

1011two to base ten
= 1(2^3) + 0(2^2) + 1(2) + 1
= 11

1574 to base twelve
powers of 12:
12, 144, 1728 , ...
1574/144 = 10 with remainder of 134
134/12 = 11 with remainder of 2

so 1574 = 10(12)^2 + 11(12) + 2
= AB2 in base 12

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