School of Science, RMIT University COSC473 Introduction to Computer Systems Semester 1, 2020 Assignment One
Please answer the following questions, showing all your working out and intermediate steps.
Use the first three letters of your given name, and the first 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 “Peter” and your surname is “Pan”, then add up PET_{26 }and PAN_{26}, and show the sum in base 26.
Example 2 — if your first name is “Peter” and your surname is “Pa”, then add up PET_{26} and PAA_{26}, and show the sum in base 26.
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) If either of these digits is a “0”, use 9 instead.
(i) how to subtract the two 5-bit binary numbers (A−B); (ii) how to translate the binary result back to decimal.
The bitwise operators AND, OR, and XOR allow for bits to be reset (to 0), set (to 1), and inverted (from 0 to 1, and from 1 to 0). Bit masks are strings of bits that allow for a single bitwise operation on particular bits. Commonly a bit string is 8 bits long (referred to as a byte).
Conventionally, bit strings are indexed from 0 staring with the rightmost digit.
Let A = xxxx xxxx_{2}, where each x is a unique bit (0 or 1).
Byte A |
x |
x |
x |
x |
x |
x |
x |
x |
Bit position |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
Find the appropriate bitmask(s) M and bitwise operator(s) for ALL byte A for the following cases, showing all your working out and intermediate steps:
For each of the above circuits:
An even-parity SECDED encoded character has been retrieved, with the hexadecimal value of BE6_{16}. Please answer the following questions, showing all your working out and intermediate steps.
You need to attempt either 6.1 or 6.2 to be eligible for an HD for this assignment, NOT BOTH.
Do some research and find out how real (floating point) numbers are represented in Binary.
If both of these digits are the same, use B = A-1.
Show in detail:
(iv) Did you lose precision/accuracy through addition? Discuss what is causing this "loss of precision" error.
Do some research and find out how a Karnauph map is used for reducing logic functions into minimal Boolean expressions.
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