We need to answer questions related to matching items, computer networks, logic gates, number systems, and program debugging. Specifically: (6) Match items from column A to column B. (7) Identify the network topology and two devices used for 'C' in the diagram. (8) Solve the given modular arithmetic expressions. (9) State the generation of computers that introduced GUIs and list the four main components of a GUI. (10) Debug and rewrite a given Pascal program. (1) Analyze a logic circuit to identify the logic gates, write the Boolean expression, construct the truth table, and determine the output for specific inputs. (2) Identify two coding systems, convert a hexadecimal number to octal, and identify the most and least significant digits of a decimal number.

Discrete MathematicsModular ArithmeticLogic GatesNumber SystemsBoolean AlgebraTruth TablesHexadecimal to Octal Conversion
2025/3/17

1. Problem Description

We need to answer questions related to matching items, computer networks, logic gates, number systems, and program debugging. Specifically:
(6) Match items from column A to column B.
(7) Identify the network topology and two devices used for 'C' in the diagram.
(8) Solve the given modular arithmetic expressions.
(9) State the generation of computers that introduced GUIs and list the four main components of a GUI.
(10) Debug and rewrite a given Pascal program.
(1) Analyze a logic circuit to identify the logic gates, write the Boolean expression, construct the truth table, and determine the output for specific inputs.
(2) Identify two coding systems, convert a hexadecimal number to octal, and identify the most and least significant digits of a decimal number.

2. Solution Steps

(6) Matching items:
A. Domain name -

2. www.e-thaksalawa.moe.gov.lk

B. Search engine -

1. yahoo

C. This is a stage of the web development process -

4. Maintaining

D. Web browser -

3. Google chrome

(7) Computer Network:
(a) Network Topology: Star topology
(b) Two devices for 'C': Hub and Switch
(8) Modular Arithmetic:
(a) 6+15 MOD 4=6+(15 MOD 4)=6+3=96 + 15 \text{ MOD } 4 = 6 + (15 \text{ MOD } 4) = 6 + 3 = 9. 9 MOD 4=19 \text{ MOD } 4 = 1. So, 6+15 MOD 4=16 + 15 \text{ MOD } 4 = 1
(b) NOT(8 MOD 2>6)NOT (8 \text{ MOD } 2 > 6). 8 MOD 2=08 \text{ MOD } 2 = 0. So, NOT(0>6)NOT(0 > 6). Since 0>60 > 6 is false, then NOT(False)=TrueNOT(False) = True.
(9) Graphical User Interface:
(a) Generation: Fourth Generation
(b) Four main components: Icons, Pointer, Windows, Menus
(10) Pascal Program Debugging and Rewriting:
```pascal
Program PositiveNo (input, output);
Var
N: Integer;
Begin
Writeln('Enter Number');
Readln(N);
If N > 0 Then
Writeln('Positive Number');
End.
```
Errors corrected:

1. Added `Var` keyword to variable declarations.

2. Changed `Read(N)` to `Readln(N)`.

3. Added `Then` keyword after `If N > 0`.

4. Changed `Writln` to `Writeln`.

5. Added a period `.` at the end of the program.

(1) Logic Circuit Analysis:
(a) Logic Gates: XOR gate, AND gate, NOT gate
(b) Boolean Expression: Z=(XY)(XY)Z = \overline{(X \oplus Y) \land (X \land Y)}
(c) Truth Table:
| X | Y | X XOR Y | X AND Y | (X XOR Y) AND (X AND Y) | Z |
|---|---|---------|---------|-------------------------|---|
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 |
(d) If X=1X=1 and Y=0Y=0, Z=1Z=1.
(2) Number Systems:
(a) Two Coding Systems: ASCII, Unicode
(b) 5E16=(5×161)+(14×160)=80+14=94105E_{16} = (5 \times 16^1) + (14 \times 16^0) = 80 + 14 = 94_{10}.
To convert 941094_{10} to octal:
94/8=1194 / 8 = 11 remainder 66
11/8=111 / 8 = 1 remainder 33
1/8=01 / 8 = 0 remainder 11
Therefore, 5E16=13685E_{16} = 136_8
(c) For the number 4000.500:
MSD (Most Significant Digit): 4
LSD (Least Significant Digit): 0

3. Final Answer

(6)
A - 2
B - 1
C - 4
D - 3
(7)
(a) Star topology
(b) Hub, Switch
(8)
(a) 1
(b) True
(9)
(a) Fourth Generation
(b) Icons, Pointer, Windows, Menus
(10)
```pascal
Program PositiveNo (input, output);
Var
N: Integer;
Begin
Writeln('Enter Number');
Readln(N);
If N > 0 Then
Writeln('Positive Number');
End.
```
(1)
(a) XOR gate, AND gate, NOT gate
(b) Z=(XY)(XY)Z = \overline{(X \oplus Y) \land (X \land Y)}
(c) See truth table in solution steps
(d) 1
(2)
(a) ASCII, Unicode
(b) 1368136_8
(c) MSD: 4, LSD: 0

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