Practice Exercise 21
  1. Write the following numbers in scientific notation: 
                           1          -268
                        3064     100,000,500,006,783
               -0.0000016384       12345678.9101112
  1. Write the same numbers above using the decimal floating point system that is presented in Chapter 24. (There are 5 digits for the mantissa, 2 digits for the exponent, which is written in excess-50 notation, and a leading 1 or 0 indicates - or +, respectively.)
  1. Which of the following numbers has the smallest value? 
               a.) -6.4 x 10-38
               b.) -6.4 x 1038
               c.) 6.4 x 10-37
               d.) 6.4 x 1037
  1. Which of the above numbers has the smallest magnitude (smallest absolute value)?
  1. Perform Floating Point addition on the following pairs of values, which are written in scientific notation. Assume that there are only 5 places of accuracy in the mantissa. 
               a.)   7.3892 x 1017
                   + 1.8901 x 1019
                   ----------------
               
               
               b.)   -7.3892 x 1017
                   + +1.8901 x 1019
                   ----------------
               
               
               c.)   7.3892 x 1014
                   + 1.8901 x 1027
                   ----------------
  1. Perform Floating Point multiplication on the following pairs of values: 
               a.    7.3892 x 1014
                   x 1.8901 x 1027
                   ---------------
               
               
               b.    3.6000 x 1014
                   x 5.0000 x 1017
                   ---------------
  1. Now perform some additions and multiplications using the decimal floating point system which we developed in Chapter 24. All results should be normalized and overflow should be indicated. Remember that the exponent is written in excess 50 notation. 
               a.   0 83021 53
                  + 0 93011 56
                  ------------
               
               
               b.   0 83021 53
                  x 0 93011 56
                  ------------
               
               
               c.   0 83021 52
                  + 1 93011 53
                  ------------
               
               
               d.   0 83021 52
                  + 0 93011 68
                  ------------
               
               
               e.   1 83021 23
                  x 1 93011 71
                  ------------
  1. Again referring to the decimal floating point system given in Chapter 24,
  1. how many representable real numbers are there? Consider all normalized, unnormalized and denormalized numbers.

     

  2. Again referring to the decimal floating point system, how many normalized numbers are there?

     

  3. How many denormalized numbers are there?
  1. Referring to the floating point addition hardware in Section 24.8:
  1. How many stages are there in the addition hardware of Fig. 7?

     

  2. What would be the expected speedup?

     

  3. How many stages are in the floating point multiplication hardware of Fig. 8?
  1. Suppose you are working a 4-bit binary number system, using excess 8 notation. Write down all 16 bit patterns and show what their values would be in unsigned binary, sign-magnitude, 2's complement and excess-8.
  1. What is the value 38 in a true binary floating point system, like the one presented in Chapter 24? The first digit is assumed since all values are stored in normalized form.