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Math Help - Converting to decimal and hexadecimal

  1. #1
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    Converting to decimal and hexadecimal

    I am having trouble with a couple of problems. Here they are:

    Convert 101100012 to decimal

    Convert 2E16 to decimal

    Convert 0010111110012 to hexadecimal.

    I can figure out the conversion, but am not sure what the sub notation means.

    Help, please...
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  2. #2
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    Lexington, MA (USA)
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    Hello, Tom!

    I assume there is a typo in #3 . . .


    1) Convert 10110001_2 to decimal

    2) Convert 2E_{16} to decimal

    3) Convert {\color{red}1}01011111001_2 to hexadecimal.

    I can figure out the conversion,
    but am not sure what the sub notation means. . . . . really?
    The subscripts represent the bases.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    1)\;\;10110001_2 is in base-2.

    We have: . 1\!\cdot\!2^7 + 0\!\cdot\!2^6 + 1\!\cdot\!2^5 + 1\!\cdot\!2^4 + 0\!\cdot\!2^3 + 0\!\cdot\!2^2 + 0\!\cdot\!2^1 + 1

    . . . . . . = \;128 + 0 + 32 + 16 + 0 + 0 + 0 + 1 \;=\;177


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    2)\;\;2E_{16} is in base-16.

    We have: . 2\!\cdot\!16^1 + 14\!\cdot\!1 \;=\;46


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    3)\;\;1010 1111 1001_2 is in base-2.

    To write it in base-16:

    . . \text{we have: }\;\underbrace{1010}_{10} \underbrace{1111}_{15} \underbrace{1001}_{9}
    . . . . . . . . . . \downarrow \quad\;\, \downarrow \quad\;\;\:\downarrow
    . . . . . . . = \;\;A\quad\,F\quad\;\;\, 9

    . . . . . . . = \;\;AF9_{16}

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  3. #3
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    THANK YOU.

    Thanks for the quick response.
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