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System uses a 6-bit 2's complement signed integer representation. What is the range of decimal values it can represent?

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  1. 9 February, 05:44
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    -32 to + 31

    Explanation:

    6 bit 2s complement representation will be of the form b1b2b3b4b5b6 where each bit is either 0 or 1.

    The largest positive number that can be represented using this scheme is 011111

    Translating this to decimal this is 1*2^4 + 1^2^3 + 1^2^2 + 1^2^1 + 1^2^0

    =16 + 8 + 4 + 2 + 1 = 31

    The smallest negative number that can be represented using this scheme is 100000

    Translating this to decimal = - 1 * 2^5 = - 32

    So the range of decimal values that can be represented is - 32 to + 31.
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