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Thread: base 10 and base 2

  1. #1

    base 10 and base 2

    I am having trouble with 8th grade math - prealgebra in base 10 and base 2. Can someone please explain it to me? Instead of the exponent being in the upper corner it is in the bottom corner. I don't understand it at all. Thank you.

  2. #2
    Elite Member
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    Quote Originally Posted by homeschoolrocks View Post
    I am having trouble with 8th grade math - prealgebra in base 10 and base 2. Can someone please explain it to me? Instead of the exponent being in the upper corner it is in the bottom corner. I don't understand it at all. Thank you.
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  3. #3
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    Quote Originally Posted by homeschoolrocks View Post
    I am having trouble with 8th grade math - prealgebra in base 10 and base 2. Can someone please explain it to me? Instead of the exponent being in the upper corner it is in the bottom corner. I don't understand it at all. Thank you.
    Do you mean something like

    [TEX]24_{10} = 11000_2[/TEX]

    If so:

    A decimal number is the sum of products of a one digit number (vulgo cipher) and a power of 10 which indicates the place of the cipher in the number. (The ciphers start always at zero and the maximum cipher is 1 smaller than the base) That means:

    [TEX]24_{10} = 2 \cdot 10^1 + 4 \cdot 10^0[/TEX]

    In a similar way a number base 2 is constructed. There are only 2 ciphers (0 and 1; see remark above). Therefore

    [TEX]11000_{2} = 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 +0 \cdot 2^1 +0 \cdot 2^0[/TEX]

    which yields 24 as a decimal number.

  4. #4

    Thanks

    Thanks for the help everybody! I am going to use this message board in the future.

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