Reference no: EM133029821

Introduction to Computer Systems

Learning outcome 1: Understanding the function and structure of key components of a computer and how they interact and communicate.
Learning outcome 2: Understanding the basics of computer logic and binary representation of data and instructions.
Learning outcome 3: Understanding, designing and simulating simple logic circuits.
Learning outcome 4: Understanding and executing simple computer arithmetic.
Learning outcome 5: Understanding the Instruction Set Architecture and simulating the fetch/execute cycles.
Learning outcome 6: Understanding Assembly Language and writing simple programmes.

Question 1

This is a research question, and you need to provide references with you answers. Please note that 200 words excluding the references is the maximum for each question.

a) Explain the impact of Turing Machines on Computer Science
b) Explain the Turing Test, also called Imitation Game
c) In the context of risk & safety when opening a computer, explain the risk of static electricity. What should you do to avoid any damage to yourself or the components of a computer?

Question 2

Assume x=5, y=2, and z=3. Evaluate the value of each of the following Boolean expressions (show details).
a) [(x > 5) NAND (y < 5)] NOR ( y ≤ z)

b) (x+y ≥ z ) XOR [( x>6) OR (z ≤ 5)]
c) [NOT( z >5) ] AND [(z=7) XOR (y<2)]

Question 3

Use the circuit given in figure below to answer the following three questions:
a) Tabulate the values of the variables X, Y and Z in the circuit for all possible values for the inputs A, B and C.

b) Work out the Boolean expression of the output Z, in terms of the inputs A, B, and C using Sum-of-products algorithm.

c) Use K-Map to work out the optimal Boolean expression of Z.

Figure 1

Question 4

A majority-rules circuit has three inputs and one output. The value of its output is 1 if and only if two or more of its inputs are 1; otherwise, the output is 0.
Design a majority-rules circuit using the sum-of-products algorithm and then use K-
Map to find the optimal expression. Draw the circuit using AND, OR and NOT gates

Question 5

Convert the natural integer 2020 in decimal to (show calculations):
a) Binary
b) Base 4
c) Octal
d) Hexadecimal

Question 6

Perform the following operations as follows

a) 34 - 78 in a signed two's complement 8-bit representation
b) 78 - 120 in a sign and magnitude binary representation

c) (F9A)16 + (7BB2)16 in hexadecimal
d) (654)8 + (566)8 in octal
e) (4111)5 - (3322)5 in base 5

Question 7
(Based on Week 3)

What is the minimum number of bits needed to represent the following? (justify your answer)

a) (512)10
b) (320)10
c) (3DE)16
d) (67)8

Question 8

Perform the following decimal operations in 8-bit two's complement arithmetic. Note that some of the answers will result in arithmetic overflow. Indicate where overflow has occurred.

a) 44
+ 101

b) 32
- 12

c) -122
-15

Question 9

Consider the IEEE standard for floating-point numbers.
a) Explain how the number of bits used for the mantissa and exponent relates to the range the precision of floating-point numbers.
b) Convert the decimal number -527.123 into the IEEE standard 32-bit format for floating-point numbers.

Question 10

Assume you have a 100x100 pixels RGB coloured image where each pixel has three colour components (red, green, and blue), and the range of each colour is [0 255]:
a) How is this image represented internally as zeroes and ones?
b) How many bytes does it take to store it?

Question 11

a) Use Booth's algorithm to work out -7 x -6 in binary
b) Using Hamming ECC, add four parity bits to the following 8-bit 1101 1001. Suppose an error occur to bit 5, demonstrate how the ECC can recover the original data.

Question 12

Using the figure below, explain what happens when a programme is being executed (max of 200 words).

Question 13

Using LMC langue, write a programme in Assembly language to input two numbers and output the result of their multiplication.