Calculate by hand A divided by B. Show all the steps necessary to achieve your answer. Assume there is a guard, a round bit, and a sticky bit, and use them if necessary. Write the final answer in both the 16-bit floating point format described in 3.11.2 and in decimal and compare the decimal result to that which you get if you use a calculator.

Problem 3.11.2

NVIDIA has a “half” format, which is similar to IEEE 754 except that it is only 16 bits wide. The leftmost bit is still the sign bit, the exponent is 5 bits wide and stored in excess-56 format, and the mantissa is 10 bits long. A hidden 1 is assumed. Write down the bit pattern assuming a modified 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.

The following table shows further pairs of decimal numbers.

Transcribed Image Text:

a. b. A 8.625 x 10¹ 1.84375 x 10⁰ B -4.875 x 10⁰ 1.3203125 x 10⁰