Consider a 1010-bit floating-point representation based on the IEEE floating-poi

Question

Consider a 1010-bit floating-point representation based on the IEEE floating-point format, with one sign bit, 55 exponent bits and 44 fraction bits.  The exponent bias follows the IEEE standard.

Interpret the bitstring 1_00000_1000 with base 2 using this 1010-bit floating-point representation and fill in the table below. You may use expressions if it's useful.

Field Mean Value The value represented by considering the exponent field to be an unsigned integer (as a decimal value) The value of the exponent after biasing (as a decimal value) The numeric weight of the exponent (as a decimal value) The value of the fraction (as a fraction such as 3/4 or the exact floating point number) The value of the significand(as a fraction s point number) The value of the number in decimal. The 's' is equal to +1 if the number is positive and -1 if it is negative. 2E uch such as 7/4 or the exact floating s*2E M

Explanation / Answer

The number is represented as 1_00000_1000 with base 2 using this 1010-bit floating-point representation.

Using this information,

1. The value of e is 0 - 31 = -31 (Since the biased exponent is 00000 and the bias value is 25 -1 = 31)

2. Here, the bias value is 25 -1 = 31. Hence the value of E is 0 + 31 = 31.

3. The numeric weight of the exponent, 2E = 20 = 1.

4. Since the result is normalized, the value of fraction is 0.1000 = 0+ 2-1 = 0.5 = 0.5

5. The value of the significand, M is = (1.1000)2 = 20 + 2-1 = 1 + 0.5 = 1.5.

6. The sign is -ve (sign bit is 1 for negative numbers, 0 for positive numbers).

Hence, the number is s * 2E * M = -1 * 1 * 1.5 = -1.5 (Ans)

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