Floating Point Representation

1. Show how each of the following floating point values would be stored using the simple model described in the textbook (14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit). Express your answer in both binary and hexadecimal:

22.5

-3.5

0.7625

25.325

2. What decimal floating point number does each of the following represent assuming it is stored using the simple model described in the textbook (14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit). Express your answer in both scientific binary format and decimal format:

13A8

2D80

0FA0

1483

3. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits,and a single sign bit for the number):

Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format.

Show how the computer would add the two floating-point numbers in part a by changing one of the numbers so they are both expressed using the same power of 2.

Show how the computer would represent the sum in part b using the given floating point representation.What decimal value for the sum is the computer actually storing? Explain.

4. Let a = 1.0 2⁹, b = 1.0 2⁹ and c = 1.0 2¹. Using the floating-point model described in the text (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits,and a single sign bit for the number), perform the following calculations, paying close attention to the order of operations. What can you say about the algebraic properties of floating-point arithmetic in our finite model? Do you think this algebraic anomaly holds under multiplication as well as addition?

b + (a + c) = (b + a) + c =

5. Show how each of the following floating point values would be stored using IEEE-754 single precision.Express your answer in hexadecimal. a) 22.5 b) 3.5 c) 0.7625 d) 25.325

Please show work and not just post answer, would like to see the process. Thank you (: