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A computer system allows only 4 binary digits after the decimal point. Write the two binary values with exactly 4 digits after the decimal point that ‘sandwich’ 0.0100112.

Using the two binary ‘sandwich’ values that you found in (ii), write down the minimum and maximum binary values that sandwich the result of 0.0100112 + 0.0100112

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  • 1 month ago
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    With 4 fraction bits, the lowest place value is 1/2^4 = 1/16.  If that 4 bit number is a number n (from 0 to 15, inclusive) then the fraction represented is n/16.  For a "sandwich", you need the 0.0100112 value to be between two consecutive fractions:

        n/16 <= 0.0100112 < (n+1)/16

        n <= 0.161792 <= n + 1              [ multiply by 16 to clear fractions ]

    So n=0 and the number if between 0/16 (0.0000b) and 1/16 (0.0001b).

    If both binary values in the 0.0100112 + 0.0100112 sum were rounded down, you get a minimum value of 0+0 = 0 = 0.0000b.

    If both values were rounded up, you'd get 1/16 + 1/16 = 2/16 = 0.0010b.

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