a) IEEE 754-2008 contains a half-precision that is only 16 bits wide. The leftmost bit is still the sign bit, the expone

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A Ieee 754 2008 Contains A Half Precision That Is Only 16 Bits Wide The Leftmost Bit Is Still The Sign Bit The Expone 1 (151.13 KiB) Viewed 39 times

a) IEEE 754-2008 contains a half-precision that is only 16 bits wide. The leftmost bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. A hidden 1 is assumed. 1 5 bits 10 bits Exp Fraction Write down the bit pattern to represent -1.5625 X 10-1 assuming a version of this format. Comment on how the range and accuracy of this 16-bit floating-point format compares to the single precision IEEE 754 standard. b) Calculate the sum of 2.6125 X 101 and 4.150390625 X 10-1 by hand, assuming A and B are stored in 16-bit half-precision. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps. c) Calculate the product of -8.0546875 X 10° and -1.79931640625 X 10-1 by hand; assuming A and B are stored in the 16-bit half precision format. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. How accurate is your result? How does it compare to the number you get if you do the multiplication on a calculator?