Question

Suppose a block of data is stored in the memory cells of the Vole from address \(0 \mathrm{x} 98\) to \(0 \mathrm{xA} 2\), inclusive. How many memory cells are in this block? List their addresses.

Short answer

There are 11 memory cells, from address \(0x98\) to \(0xA2\).

Step-by-step solution

Convert Start and End Addresses to Decimal

The given start address is \(0x98\) and the end address is \(0xA2\). Convert these hexadecimal values to decimal to make it easier to calculate the number of memory cells. \(0x98\) is equal to \(9 \times 16 + 8 = 152\) in decimal, and \(0xA2\) is equal to \(10 \times 16 + 2 = 162\) in decimal.

Calculate the Number of Memory Cells

To find the number of memory cells, subtract the decimal start address from the decimal end address and add 1 (since both addresses are inclusive). Therefore, the calculation is \(162 - 152 + 1 = 11\) memory cells.

List the Memory Addresses

To list the addresses, convert each decimal number from 152 to 162 back to hexadecimal. The addresses are \(0x98\), \(0x99\), \(0x9A\), \(0x9B\), \(0x9C\), \(0x9D\), \(0x9E\), \(0x9F\), \(0xA0\), \(0xA1\), and \(0xA2\).

Key concepts

Hexadecimal Conversion

Hexadecimal is a base-16 number system that uses 16 symbols - the numbers 0-9 and the letters A-F, where A represents 10, B represents 11, and so on, up to F which stands for 15. Each digit represents a power of 16.
For example, in the weight decimal representation:

• Hexadecimal 98 means: 9 * 16^1 + 8 * 16^0, which equals 152 in decimal.
• Hexadecimal A2 means: A(10) * 16^1 + 2 * 16^0, which is equal to 162 in decimal.

The beauty of hexadecimal is its efficiency in representing large numbers, especially useful in computing for addressing memory. It's a way of expressing memory addresses that is compact yet still fairly readable.
When converting from hexadecimal to decimal, you multiply each digit by a power of 16, with the rightmost digit being 16^0. It makes binary numbers more manageable by summarizing every four binary bits with a single hex digit.

Memory Cells

Memory cells are the smallest units of storage in a computer's memory. Each cell has its own unique address, which is analogous to a mailbox number, allowing data retrieval and storage.
In computing, the memory cells are crucial as they hold the data that the CPU processes. Usually, memory addresses are represented in hexadecimal because this system aligns well with binary representation, making them efficient and compact.
Suppose a computational process needs to access data from one memory cell; it uses the specific address to find the right cell. In our exercise, the memory cells range from address 0x98 to 0xA2, which when counted inclusively, results in 11 different memory cells.
The inclusion of both starting and ending cells explains why we add one after subtracting the starting address from the ending address when counting cells. This ensures that every part of the data block is accounted for in the memory allocation.

Computer Architecture

Computer architecture is like the skeleton of a computer—it defines how a computer is organized and how it manages data, from storage to processing. At its core, computer architecture involves structuring the hardware components and determining the interconnections between those components.
Memory and its addressing are key components in computer architecture. The way memory is addressed and structured affects how quickly and efficiently data can be accessed and processed.
In this context, understanding memory addresses is essential. They help the CPU fetch the correct instructions and data, facilitating operations efficiently. This efficiency is partly due to the binary and hexadecimal systems, which optimize representation and reduce the complexity of hardware designs.
By understanding memory addressing, computer engineers can design systems that effectively manage performance and resource allocation. This especially matters in designing CPUs and memory interactions—planning and knowing where each byte of data is stored are key to optimizing computing speed and capacity.