We need to answer multiple-choice questions related to computer architecture, networking, number systems, logic gates, and the boot process.

Discrete MathematicsNumber SystemsBinaryHexadecimalBCDLogic GatesASCIIBoolean Algebra
2025/6/29

1. Problem Description

We need to answer multiple-choice questions related to computer architecture, networking, number systems, logic gates, and the boot process.

2. Solution Steps

Question 6: Access speed in ascending order.
Register memory is the fastest, followed by cache memory, and then main memory. Therefore, the correct order is Register memory, Cache memory, Main Memory.
Question 7: Network topology where a single computer breakdown doesn't affect the whole network when connected to a centralized device by a single cable.
This describes a bus topology.
Question 8: Decimal 80310 in BCD code.
In BCD, each decimal digit is represented by its 4-bit binary equivalent.
8 -> 1000
0 -> 0000
3 -> 0011
1 -> 0001
0 -> 0000
So, 80310 in BCD is 1000 0000 0011 0001
0
0
0

0. Therefore the option is (1) $100000100011_{BCD}$

Question 9: ASCII code of 'C' is
1
0
0
0
0
1

1. Find the character for

1
0
0
0
1
1

1. Since ASCII codes are consecutive for letters, 'C' is 1000011, 'D' would be 1000100, 'E' is 1000101, 'F' is 1000110, and 'G' is

1
0
0
0
1
1
1.
Question 10: Compare A (A916A9_{16}) and B (10011111210011111_2).
Convert A916A9_{16} to decimal: 10161+9160=160+9=16910 * 16^1 + 9 * 16^0 = 160 + 9 = 169.
Convert 10011111210011111_2 to decimal: 127+026+025+124+123+122+121+120=128+16+8+4+2+1=1591 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 16 + 8 + 4 + 2 + 1 = 159.
Since 169 > 159, A is larger than B.
Question 11: Convert decimal 255 to binary.
255 can be written as 2812^8 - 1.
27+26+25+24+23+22+21+202^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0
128+64+32+16+8+4+2+1=255128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255
So the binary representation is
1
1
1
1
1
1
1
1.
Question 12: Identify the logic gate from the truth table.
The truth table shows that the output is 1 only when both inputs are 0, otherwise the output is

0. This corresponds to a NOR gate.

Question 13: Given a NOR gate with input A=1, what is the output Q?
In a NOR gate, if either input is 1, the output is

0. Since A is 1, the output Q will be 0, regardless of the value of B.

Question 14: Booting process after turning on the computer.
The correct order is: After power-up, the self-test (POST) is run, and then the system files (MBR) are loaded into Random Access Memory (Main Memory).

3. Final Answer

6. (4) Register memory, Cache memory, Main Memory

7. (2) Bus topology

8. (1) 100000100011BCD

9. (1) G

1

0. (2) Number (A) is larger than number (B)

1

1. (2) 11111111

1

2. (2) NOR Gate

1

3. (1) O

1

4. (1) After power-up, the self-test (POST) is run and then system files (MBR) are loaded into Random Access Memory (Main Memory)

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