ZIMSEC O Level Computer Science - Data Representation, ASCII, Network & Internet Technologies

Question 1

A computer system uses 16-bit signed integer representation. What is the largest positive decimal number that can be stored, and how would -50 be represented in two's complement?

Accepted Answer

Largest positive number: 2^(16-1) - 1 = 32767. Two's complement of -50: 1. Convert 50 to binary (16-bit): 0000000000110010. 2. Invert all bits: 1111111111001101. 3. Add 1: 1111111111001110.

Question 2

Explain the concept of "overflow" in the context of fixed-point binary arithmetic. Provide an example using 8-bit signed two's complement where adding two positive numbers results in an overflow.

Accepted Answer

Overflow occurs when the result of an arithmetic operation exceeds the maximum range that can be represented with the given number of bits. For 8-bit signed two's complement, the range is -128 to 127. Example: 70 (01000110) + 60 (00111100) = 130. The binary addition would be 01000110 + 00111100 = 10000010. The leading bit is 1, indicating a negative number (-126), which is incorrect, demonstrating overflow.

Question 3

A custom character encoding scheme uses 6 bits per character. How many unique characters can be represented? If a text file contains 1000 characters using this scheme, what is the minimum file size in kilobytes, assuming no compression?

Accepted Answer

Number of unique characters: 2^6 = 64. File size: 1000 characters * 6 bits/character = 6000 bits. 6000 bits / 8 bits/byte = 750 bytes. 750 bytes / 1024 bytes/KB = 0.732 KB (approximately).

Question 4

Discuss the limitations of ASCII in representing global languages. How does Unicode address these limitations, and what are the implications of using variable-length encodings like UTF-8?

Accepted Answer

ASCII is limited to 128 characters, primarily English alphabet, numbers, and symbols, making it insufficient for languages with larger character sets (e.g., Chinese, Arabic). Unicode provides a unique number for every character, no matter the platform, program, or language. UTF-8 is a variable-length encoding, meaning characters can take 1 to 4 bytes. Implications include: backwards compatibility with ASCII (single-byte characters are the same), efficient storage for common characters, but more complex processing due to variable length.

Question 5

A network administrator is setting up a new office with 50 computers. They need to assign IP addresses using a single subnet from the 192.168.1.0/24 range. Design a subnetting scheme that accommodates all computers and allows for future expansion (at least 20 more devices). Identify the subnet mask, network address, broadcast address, and the range of usable IP addresses.

Accepted Answer

To accommodate 70 devices (50 + 20), we need at least 2^n - 2 >= 70, so n=7 (2^7 = 128). This means 7 bits for host addresses, leaving 32-7 = 25 bits for the network. Subnet mask: /25 or 255.255.255.128. Network address: 192.168.1.0. Broadcast address: 192.168.1.127. Usable IP range: 192.168.1.1 to 192.168.1.126.

Question 6

Compare and contrast the OSI model and the TCP/IP model. For each model, identify the layer responsible for reliable data transfer and explain how it achieves this reliability.

Accepted Answer

OSI Model: 7 layers (Physical, Data Link, Network, Transport, Session, Presentation, Application). TCP/IP Model: 4 layers (Network Access, Internet, Transport, Application). Reliable data transfer: OSI - Transport Layer (Layer 4), TCP/IP - Transport Layer. Both achieve reliability through mechanisms like segmentation, sequencing, acknowledgements, flow control, and error detection/retransmission (e.g., TCP).

Question 7

A user is experiencing slow internet speeds and frequent disconnections. Describe three potential causes related to network and internet technologies, and for each, suggest a troubleshooting step.

Accepted Answer

1. **Cause: Wi-Fi interference.** Other devices (microwaves, cordless phones) or neighboring Wi-Fi networks can interfere. **Troubleshooting:** Change Wi-Fi channel, move router, reduce distance to router. 2. **Cause: Congested network.** Too many devices using bandwidth simultaneously. **Troubleshooting:** Limit simultaneous downloads/streaming, upgrade internet plan, implement QoS (Quality of Service) on router. 3. **Cause: Faulty cabling/hardware.** Damaged Ethernet cables, old router/modem. **Troubleshooting:** Replace cables, restart/update router firmware, test with different devices.

Question 8

Explain the difference between a MAC address and an IP address. In what layer of the OSI model does each operate, and why are both necessary for network communication?

Accepted Answer

MAC Address: A physical, unique identifier assigned to network interfaces (e.g., NICs) by the manufacturer. Operates at the Data Link Layer (Layer 2) of the OSI model. IP Address: A logical address assigned to devices on a network, used for routing data across different networks. Operates at the Network Layer (Layer 3) of the OSI model. Both are necessary because MAC addresses are used for local communication within a network segment, while IP addresses are used for global communication across interconnected networks (internetworking). IP addresses allow devices to be located, and MAC addresses allow data to be delivered to the correct device once it reaches the local network.

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