Some numbers can be represented in floating point representation in different wa

Question

Some numbers can be represented in floating point representation in different ways. For fractions with repeating parts, any representation must be approximate and the more bits used, the closer the approximation. For the following repeating binary fractional representations, find the exponent in base 10 of the error actual -approximate when the approximate is limited to the given number of bits. (8 points) 30.00101101 17 Base 10 exponent of 8 bit approximation 17 Base 10 exponent of-- 16 bit approximation- 17 30.1001 Base 10 exponent of- 4 bit approximation- Base 10 exponent of8 bit approximation- Base 10 exponent of - 12 bit approximation- 10 0.01010 10 Base 10 exponent of 5 bit approximation 31 Base 10 exponent of- 10 bit approximation-

Explanation / Answer

a) 3/17 = 0.1764705882

The binary representation of 0.1764705882 = 0.00101101001011010011

b) 3/5 = 0.6

The binary representation if 0.6 = 0.1001100110011001101

c) 10/31 = 0.3225806452

The binary representation if 10/31 = 0.0101001010010100101

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