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

*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).

**[9 points]**Find the eight bit 2’s complementary representation for the following decimal numbers: a) 122 b) -122 c) 55**[3 points]**Is there a relationship between ASCII character representation of the decimal digits from 0 to 9 and their BCD representation?**[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?**[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?

- 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?