1.

Convert the following binary numbers to decimal form:

2.

Convert the following binary numbers to decimal form:

3.

Find the first five binary digits of (0.1) ₁₀. Obtain values for the absolute and relative errors in yours results.

4.

Convert the following:

1. decimal numbers to binary numbers form:

   
   

2. decimal numbers to hexadecimal decimal numbers:

   
   

3. hexadecimal numbers to both decimal and binary:

   
   

5.

What is the absolute error in approximating 1/3 by 0.3333? What is the corresponding relative error?

6.

Evaluate the absolute error in each of the following calculations and hence give the answer to a suitable degree of accuracy:

1. 9.01+9.96,

2. 4.65 ?3.429,

3. 0.7425 0.7199,

4. 0.7078 0.87.

7.

Find the absolute and relative errors in approximating ? by 3.1416. What are the corresponding errors in the approximation 100 ? ?314.16?

8.

Calculate the error, relative error, and number of significant digits in the following approximations, with p ?x:

1. x=25.234, p=25.255.

2. x=e, p=19/7.

3. x= , p=1.414.

9.

Write each of the following numbers in (decimal) floating-point form, starting with length m and exponent e:

10.

Find the absolute error in each of the following calculations (all numbers are rounded):

1. 187.2+93.5.

2. 0.281 3.7148.

3. .

4. .

11.

Express the base of natural logarithm e as a normalized floating-point number, using both chopping and symmetric rounding for each of the following systems:

1. base 10 with 4 significant figures.

2. base 10 with 7 significant figures.

3. base 2 with 10 significant...