Calculate 1.666015625 10 0 (1.9760 10 4 + -1.9744 10 4 ) by
Question:
Calculate 1.666015625 × 100 × (1.9760 × 104 + -1.9744 × 104) by hand, assuming each of the values are stored in the 16-bit half precision format described in Exercise 3.27 (and also described in the text). Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.
Exercise 3.27
IEEE 754-2008 contains a half precision that is only 16 bits wide. The left most 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. Write down the bit pattern to represent -1.5625 × 10-1 assuming a version of this format, which uses an excess-16 format to store the exponent. Comment on how the range and accuracy of this 16-bit floating point format compares to the single precision IEEE 754 standard.
Step by Step Answer:
Computer Organization and Design The Hardware Software Interface
ISBN: 978-0124077263
5th edition
Authors: David A. Patterson, John L. Hennessy