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Math Help - The range of numbers of an n-bit cell in general?

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    The range of numbers of an n-bit cell in general?

    With unsigned binary representation, what is the range of numbers as written in binary
    and in decimal for the following cells?

    (e)an n-bit cell in general

    This problem comes from the Computer Systems by Warford book if that helps. I don't know how to write it. I know for example a three bit cell the answer is:
    in binary 000-111 and decimal 0 to 7.
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  2. #2
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    Re: The range of numbers of an n-bit cell in general?

    Quote Originally Posted by lamentofking View Post
    With unsigned binary representation, what is the range of numbers as written in binary
    and in decimal for the following cells?

    (e)an n-bit cell in general

    This problem comes from the Computer Systems by Warford book if that helps. I don't know how to write it. I know for example a three bit cell the answer is:
    in binary 000-111 and decimal 0 to 7.
    in general, in base k, n digits can represent kn numbers so if 0 is to be your first number you have the range of [0,kn-1].

    for binary k=2
    for decimal k=10
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    Re: The range of numbers of an n-bit cell in general?

    Quote Originally Posted by romsek View Post
    in general, in base k, n digits can represent kn numbers so if 0 is to be your first number you have the range of [0,kn-1].

    for binary k=2
    for decimal k=10
    And for two's complement binary representation, with a 7-bit cell, would the range be [-7,6]? I'm guessing the formula could be [-n, to n-1], where n is the number of bits in the cell. but that's decimal . I don't know how to write it for binary.
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    Re: The range of numbers of an n-bit cell in general?

    Quote Originally Posted by lamentofking View Post
    And for two's complement binary representation, with a 7-bit cell, would the range be [-7,6]? I'm guessing the formula could be [-n, to n-1], where n is the number of bits in the cell. but that's decimal . I don't know how to write it for binary.
    [-2^{n-1}, 2^{n-1}-1] for an n bit, binary string, so for n=7 the range is [-2^6,2^6-1]=[-64,63]
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