# Calculate (3.41796875 10 -3 6.34765625 10 -3 ) 1.05625 10 2 by hand,

## Question:

Calculate (3.41796875 10^{-3} × 6.34765625 × 10^{-3}) × 1.05625 × 10^{2} 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:

**Related Book For**

## Computer Organization and Design The Hardware Software Interface

**ISBN:** 978-0124077263

5th edition

**Authors:** David A. Patterson, John L. Hennessy