The problem consists of several sub-problems covering various topics in computer science and information technology, including: i. Identification of hardware technology used in second-generation computers and comparison between second and third generation computers. ii. Listing ways ICT helps in education and characteristics of information. iii. Hexadecimal and octal addition and octal to binary conversion. iv. Logic gate circuit analysis to determine the output. v. Matching computer components to their respective ports. vi. Identification of coding systems used by computers. vii. Completing a pseudocode for determining if a number is even or odd.

Discrete MathematicsNumber SystemsBoolean AlgebraComputer Science FundamentalsBinaryOctalHexadecimalLogic Gates
2025/5/6

1. Problem Description

The problem consists of several sub-problems covering various topics in computer science and information technology, including:
i. Identification of hardware technology used in second-generation computers and comparison between second and third generation computers.
ii. Listing ways ICT helps in education and characteristics of information.
iii. Hexadecimal and octal addition and octal to binary conversion.
iv. Logic gate circuit analysis to determine the output.
v. Matching computer components to their respective ports.
vi. Identification of coding systems used by computers.
vii. Completing a pseudocode for determining if a number is even or odd.

2. Solution Steps

i. a. The major hardware technology used in second-generation computers was the transistor.
b. Two differences between second and third-generation computers are:

1. Second-generation computers used transistors, while third-generation computers used integrated circuits (ICs).

2. Second-generation computers were faster and smaller than first-generation computers but slower and larger than third-generation computers.

ii. a. Four ways ICT helps in the field of education are:

1. Access to online learning resources.

2. Enhanced communication between students and teachers.

3. Interactive learning tools and simulations.

4. Improved research capabilities.

b. Four characteristics of information are:

1. Accuracy

2. Timeliness

3. Relevance

4. Completeness

iii. a. 4BF16+345684BF_{16} + 3456_8
First, convert both numbers to decimal:
4BF16=(4×162)+(11×161)+(15×160)=(4×256)+(11×16)+(15×1)=1024+176+15=1215104BF_{16} = (4 \times 16^2) + (11 \times 16^1) + (15 \times 16^0) = (4 \times 256) + (11 \times 16) + (15 \times 1) = 1024 + 176 + 15 = 1215_{10}
34568=(3×83)+(4×82)+(5×81)+(6×80)=(3×512)+(4×64)+(5×8)+(6×1)=1536+256+40+6=1838103456_8 = (3 \times 8^3) + (4 \times 8^2) + (5 \times 8^1) + (6 \times 8^0) = (3 \times 512) + (4 \times 64) + (5 \times 8) + (6 \times 1) = 1536 + 256 + 40 + 6 = 1838_{10}
Now add the decimal values:
121510+183810=3053101215_{10} + 1838_{10} = 3053_{10}
So, 4BF16+34568=3053104BF_{16} + 3456_8 = 3053_{10}
b. Convert 5028502_8 to binary.
Convert each octal digit to its 3-bit binary equivalent:
58=10125_8 = 101_2
08=00020_8 = 000_2
28=01022_8 = 010_2
Combine the binary equivalents:
5028=1010000102502_8 = 101000010_2
iv. Analyzing the logic gate circuit:
The circuit consists of two NOT gates, two AND gates, and one OR gate.
Let the inputs be X, Y, and Z.
The outputs of the NOT gates are NOT X and NOT Y.
The inputs to the AND gates are (NOT X, Z) and (NOT Y, Z).
The outputs of the AND gates are (NOT X AND Z) and (NOT Y AND Z).
The inputs to the OR gate are (NOT X AND Z) and (NOT Y AND Z).
The final output F is (NOT X AND Z) OR (NOT Y AND Z).
Using Boolean algebra:
F=(XZ)(YZ)F = (\overline{X} \land Z) \lor (\overline{Y} \land Z)
F=Z(XY)F = Z \land (\overline{X} \lor \overline{Y})
F=Z(XY)F = Z \land \overline{(X \land Y)}
If we assume X = 1, Y = 1, Z =

1. Then NOT X = 0, NOT Y = 0

(NOT X AND Z) = (0 AND 1) = 0
(NOT Y AND Z) = (0 AND 1) = 0
F = (0 OR 0) = 0
If we assume X = 0, Y = 0, Z =

0. Then NOT X = 1, NOT Y = 1

(NOT X AND Z) = (1 AND 0) = 0
(NOT Y AND Z) = (1 AND 0) = 0
F = (0 OR 0) = 0
If we assume X = 1, Y = 0, Z =

1. Then NOT X = 0, NOT Y = 1

(NOT X AND Z) = (0 AND 1) = 0
(NOT Y AND Z) = (1 AND 1) = 1
F = (0 OR 1) = 1
If we assume X = 0, Y = 1, Z =

1. Then NOT X = 1, NOT Y = 0

(NOT X AND Z) = (1 AND 1) = 1
(NOT Y AND Z) = (0 AND 1) = 0
F = (1 OR 0) = 1
If Z = 0, then F = 0 regardless of the values of X and Y. If Z=1Z = 1 and X=0X=0 or Y=0Y = 0 then F=1F=1, otherwise F=0F=0 if X=1X=1 and Y=1Y=1.
v. Matching column A with B:

1. Keyboard - B (PS/2 Port). Some keyboards might also connect via USB, but PS/2 is most associated with older keyboards.

2. Printer - C (Parallel Port). Parallel port is used for printers.

3. Router - D (Network Port (RJ 45)). Routers connect to the network.

4. Monitor - A (Video Port). Monitors connect via VGA, HDMI, DVI, or DisplayPort, which are all video ports.

vi. The coding systems used by the computer include:
ASCII (American Standard Code for Information Interchange), Unicode, EBCDIC (Extended Binary Coded Decimal Interchange Code).
vii. Completing the pseudocode:
Begin
Input X
IF X mod 2 = 0 Then
Print "X is even number"
Else
Print "X is odd number"
End

3. Final Answer

i. a. Transistor
b.

1. Second-generation computers used transistors, while third-generation computers used integrated circuits (ICs).

2. Second-generation computers were faster and smaller than first-generation computers but slower and larger than third-generation computers.

ii. a.

1. Access to online learning resources.

2. Enhanced communication between students and teachers.

3. Interactive learning tools and simulations.

4. Improved research capabilities.

b.

1. Accuracy

2. Timeliness

3. Relevance

4. Completeness

iii. a. 3053103053_{10}
b. 1010000102101000010_2
iv. F=(XZ)(YZ)=Z(XY)F = (\overline{X} \land Z) \lor (\overline{Y} \land Z) = Z \land \overline{(X \land Y)} (or a truth table showing the output for different inputs to X,Y,Z)
v. 1-B, 2-C, 3-D, 4-A
vi. ASCII, Unicode, EBCDIC
vii.
IF X mod 2 = 0 Then
Print "X is even number"
Else
Print "X is odd number"

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