Understanding the Capacity and Design of a 24-Bit Address Memory with 8-Bit Word Size

Introduction

When dealing with memory systems, understanding the capacity and design considerations is crucial for optimizing system performance and efficiency. This article will focus on a specific memory configuration featuring a 24-bit address and an 8-bit word size. We will explore how many bytes can be stored in this memory and how to determine the number of memory chips required for its construction using 1K 1-bit RAM chips.

Part A: Calculating the Memory Capacity

A memory's capacity is determined by its address space and the word size (bits) that each address represents. For a 24-bit address memory with an 8-bit word size, we can calculate the total capacity as follows:

Address Space

24-bit Address

With a 24-bit address, the memory can address 2^{24} different locations. This can be calculated as:

2^{24} 16,777,216 addresses

Word Size

Each word is 8 bits, which is equivalent to 1 byte. Therefore, each address corresponds to 1 byte of data.

Total Memory Size

The total number of bytes that can be stored in this memory is:

16,777,216 bytes

This can also be expressed as 16 MiB (megabytes).

Part B: Constructing the Memory with 1K 1-bit RAM Chips

Let's now consider how this memory capacity can be achieved using 1K 1-bit RAM chips. Each chip can store 1024 bits (1 kilobit).

Chip Requirements

1K 1-bit RAM Chip

Each chip can store 1024 bits:

1K 1024 bits

Total Bits in Memory

The total number of bits in the 24-bit address memory is:

16,777,216 bytes times; 8 bits/byte 134,217,728 bits

Number of Chips Required

To determine the number of 1K 1-bit chips needed, we divide the total number of bits by the number of bits per chip:

Number of chips 134,217,728 bits / 1024 bits/chip 131,072 chips

Thus, 131,072 memory chips are required to construct this memory.

Summary of Answers

A: The memory can store 16,777,216 bytes or 16 MiB.

B: 131,072 memory chips are required to construct this memory using 1K 1-bit RAM chips.

Conclusion

Understanding the capacity and design of a memory system with specific address and word sizes is essential for efficient memory management. This example demonstrates the step-by-step process of calculating memory capacity and determining the required number of memory chips, providing insights that are valuable for both hardware design and software optimization.