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Math Help - University Maths question

  1. #1
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    University Maths question

    Can anyone help me out with this badboy?


    Find a method for converting a repeating expansion (with any period
    t and any numbers of non-repeating digits between the point and the rst repeating digit) from binary tohexadecimal, without converting to base ten at any stage. Then convert the repeating binaryexpansion
    10101.001101 (the last 5 digits 01101 are repeating)
    to hexadecimal (without using base ten). [Note the one non-repeating digit before the re-
    peating part.]

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  2. #2
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    Re: University Maths question

    Hello, lucasterry!

    Find a method for converting a repeating decimal expansion (with any period and any number of non-repeating digits
    between the decimal point and the 1st repeating digit) from binary to hexadecimal, without converting to base ten.
    Then convert the repeating binary expansion 10101.0\overline{01101} to hexadecimal (without using base ten).

    To convert 11101001011100.011_2 to hexadecimal, group the digits is sets of four,
    . . starting at the decimal point and reading to the left and right.

    We have: . 11|1010|0101|1100|.0110|

    Convert each group to hexadecimal: . \underbrace{11}_3|\underbrace{1010}_{10}| \underbrace{0101}_5|\underbrace{1100}_{12}|. \underbrace{0101}_6|

    Therefore: . 3A5C.6_{16}



    We are given: . 10101.0\overline{01101}_2

    We have: . \underbrace{1}_1|\underbrace{0101}_5|.\underbrace{  0011}_3|\underbrace{0101}_5|\underbrace{1010}_{10}  |\underbrace{1101}_{13}|\underbrace{0110}_6| \underbrace{1011}_{11}|\underbrace{0101}_5| \underbrace{1010}_{10}|\underbrace{1101}_{13}| \hdots

    Therefore: . 15.3\,\overline{5AD6B}_{16}

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