AP/ITEC1000 Sections A and B “Introduction to Information Technologies”

The total number of points for this assignment is 130. Points for each question are [as indicated]. This Assignment is worth five percent (5%) of your total grade.

Please type in your answers in the Answer Form provided. 50% mark deduction for not using the Answer Form. Answers not typed in will not be accepted or marked.

Please circle your section on the Answer Form. Append your handwritten worksheets to your Answer Form.

Assignments without worksheets appended will not be accepted or marked. Textbook Reading: Chapters 4 and 5 (Lecture notes 3, 4 and 5).

  1. [9 points] Find the eight bit 2’s complementary representation for the following decimal numbers: a) 122                        b)     -122                           c)     55
  2. [3 points] Is there a relationship between ASCII character representation of the decimal digits from 0 to 9 and their BCD representation?
  3. [5 points] Consider a hypothetical computer system. A two-byte memory space is used for a sign-and- magnitude representation of integers with BCD, and the sign is stored in MSB. What is the range of signed integers in base 10 that can be so represented?
  4. [18 points] Consider the two following decimal numbers: 14,645 and -8,731
  • Convert these numbers to 9’s complement five-digit representation and show all the steps
  • Find the sum of the two numbers in 9’s complement arithmetic showing all the steps and convert the sum back to decimal
  • Was there a carry or overflow condition in your calculation? Explain
  • Convert the initial two numbers to 10’s complement five-digit representation and show all the steps
  • Find the sum of the two numbers in 10’s complement arithmetic showing all the steps and convert the sum back to decimal
  • Compare the two procedures and explain the difference of addition in 9’s and 10’s complement. Which one is easier to implement?

     5. 6 points] Provide the Packed Decimal representation of the following decimal numbers: a)

          -75                             b)           7657                         c)     -4327

    6. [6 points] What number is represented in 9’s complement by:

  • 2777 (four-digit 9′ complement representation) b) 617 (three-digit 9′ complement representation)

     7. [6 points] Perform the calculation 99.685 + 0.99685 using the decimal floating point representation                              SEEMMMM where S is the sign (0 for “plus”, 1 for “minus”) EE is the decimal exponent in excess-50 notation and              MMMMM is the five-digit Show all steps and explain the result.

    8. [18 points] Convert the following binary numbers to floating-point format using single-precision IEEE 75

    Convert your answer to hexadecimal format. a) 0111 b)     -111.110101         c)     -0.0101101

   9. [21 points] Convert the following hexadecimal numbers to floating-point format using single-precision IEEE 754

   format. Convert your answer to hexadecimal format.

    a) 312A b)     -B32.6                      c)     -0.00C2

    10. [7 points] Convert the following decimal number to floating-point format using single-precision IEEE 754           Express your answer in hexadecimal format. Do the conversions with 8 bits of precision in the mantissa.

      -21.102

   11. [21 points] The following numbers are in IEEE 754 single-precision floating-point format. What decimal numbers do they represent?

  1. a) C3C2E00016 b)     463B540016                 c)     BEF8000016

   12. [3 points] (a) What is the collating sequence?

  • Is it the same in the different conversion/representation tables? Give
  • In what operations it may matter?

13. [2 points] True or False: Double precision floating point format can store all real numbers in the range 2-126 to 2127.

14. [1 point] True or False: In ten’s decimal complement, negative numbers are represented by

15. [2 points] The magnitude of a floating point number is known as the:                                    

16. [2 points] A number too close to zero to store in a computer is an example of what condition?

SAMPLE/PARTIAL SOLUTION

Introduction-to-IT-fff ...................Assign 2 (1)