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COSC2473 Introduction To Computer Systems And Platform Technologies

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Question 1 — Number Systems

Please answer the following questions, showing all your working out and intermediate steps.

  1. Convert the last five digits of your RMIT student number to binary. For example, if your student number is “s1234567”, then convert 3456710 to binary, octal, and hexadecimal.

b.Convert the last five digits of your RMIT student number to base 12, where 1010=A13, 1110=B13.

Consider a base 26 number system wherein the letters of the alphabet are the digits. That is, A26=010, B26=110, C26=210, … Z26=2510. Use the first three letters of your given name, and the last three letters of your surname as numbers in the base 26 system. Add these two base 26 numbers together to obtain the sum (in base 26). Show all your working out and intermediate steps.

Note: If one of these has less than three letters, repeat the last letter, e.g. LI become LII.

Example 1 — if your first name is “Lara” and your surname is “Croft”, then add up LAR26 and OFT26, and show the sum in base 26.

Example 2 — if your first name is “Lara” and your surname is “Ft”, then add up LAR26 and FTT26, and show the sum in base 26.

Question 2 — Binary Addition and Subtraction (13 marks)

Please answer the following questions, showing all your working out and intermediate steps. For this question, use the last two digits of your student number. (For example, if your student number is “s1234567”, then A=7 and B=6; −A=−7 and −B=−6.) If either of these digits is a “0”, use 9 instead.

  1. Convert decimal numbers A and B to 4-bit binary numbers; and −A and −B to 6-bit binary numbers.
  2. Show how to add together the two 4-bit binary numbers (A+B) and state whether the answer is valid to 4-bit arithmetic.
  3. Show how to use 2’s complement 6-bit arithmetic to compute (−A−B). Show how to translate the binary result back to decimal.

Carrier Sense Multiple Access/Collision Detect (CSMA/CD) is a major protocol used in Ethernet and standardised as 802.3

  1. Briefly explain how CSMA/CD works.
  2. How is the back off time calculated in the event of a collision?
  3. What is CSMA/CA (Carrier Sense Multiple Access/Collision Avoidance) and what is the major difference compared to CSMA/CD.

Do some research and find out how real (floating point) numbers are represented in Binary.

  1. Devise your own 16-bit representation for floating point numbers. Draw a diagram of your representation and explain what the various bits are used for.
  2. Show how the numbers 1, 10, and 1/3 are represented in your system.
  3. If your student number is “s1234567”, then
  • A=7 and B=6
  • x = A + B/10 = 7 + 6/10 = 7.6
  • y = B + A/10 = 6 + 7/10 = 6.7

If either of these digits is a “0”, use 9 instead.

(i) Show how x and y would be represented using your 16-bit representation.

(ii) Show in detail, the various steps needed to add together the two numbers x and y. d. When adding up a large number of floating point numbers, in what order should they be added together to get the most accurate result? Explain why with an example

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