Question 8: Round the following binary numbers to nearest 1/8. Perform round down action in case of "Half way": a) 1011.1111001 b) 11001.101100000
Question 8:
Round the following binary numbers to nearest 1/8. Perform round down action in case of "Half way":
a) 1011.1111001
b) 11001.101100000
a) 1011.1111001
The binary number 1011.1111001 is rounded to nearest 1/8 is 1011.875 in the decimal representation.
Explanation:
In the binary representation, rounding to nearest 1/8 is equivalent to the rounding of first three decimal places. To round a number, first three bits after decimal point are to be evaluated. If third bit is 0, then the number is rounded to down. If third bit is 1 and second bit is also 1, then the number is rounded up. If third bit is 1 and second bit is 0, then the number is rounded to nearest even number.
Therefore In this case, third bit after decimal point is 1 and second bit is 1, hence the number is rounded up to 1011.875 in the binary representation.
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