1. Find the 32-bit single-precision representation for each number. Assume the format 1 2 23 e  where 1 unless the number is zero. a XXXXXXXXXX b. −18.1875 c. 2.7   2.  Assume you are performing...

1. Find the 32-bit single-precision representation for each number. Assume the format

<sub>1

2

23</sub>

^e
 where

₁
unless the number is zero.

a. 12.0625

b. −18.1875

c. 2.7

2.  Assume you are performing decimal arithmetic with
 significant digits. Using rounding, perform the following calculations:

<sup>3

4</sup>

3. Using four significant digits, compute the absolute and relative error for the following conversion to floating point form.

<sub>1

1</sub>

<sub>2

2</sub>

4. Verify the error bounds for addition and multiplication. Use

5. Assume we are using IEEE double-precision arithmetic.

 What is the error bound in computing the sum of 20 positive floating point numbers?

 What is the error bound in computing the product of 20 floating point numbers?

6. If

<sub>min

max</sub>
 find

_min
and

_max

7. By constructing a counterexample, verify that floating-point addition and multiplication,
 and
 do not obey the distributive law

8. Show that, unlike the operation
 the operation
 is not associative. In other words
 in general.