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6 August, 13:11

Which of the following representations in two's complement notation represents the smallest value?

A. 00000010 B. 11110000 C. 00000001 D. 11111111

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  1. 6 August, 15:28
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    B. 11110000

    Explanation:

    Representing each of the binary inputs in twos complement format as a decimal number:

    A. 00000010 = 1*2^1 = 2

    B. 11110000:

    Getting the 2s complement of this number: 00001111 + 1 = 00010000

    Converting to decimal = 1 * 2^4 = 16

    So the original number is negative of this, namely - 16

    C. 00000001 = 1 * 2^0 = 1

    D. 11111111:

    Getting the 2s complement of this number: 00000000 + 1 = 00000001

    Converting to decimal = 1 * 2^0 = 1

    So the original number is negative of this, namely - 1

    Of the given numbers, B. 11110000 (-16) is the smallest.
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