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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