How many address lines and input-output data lines are needed in a 2k × 16 memory unit?
Understanding Memory Unit Architecture
A memory unit is characterized by its capacity, which is typically given in the format 'Number of Locations × Word Size'. In this question, we are given a memory unit specified as 2k × 16.
- Number of Locations: The first part, "2k", represents the number of distinct memory locations that can store data. The 'k' here stands for kilo, which in digital contexts usually means $2^{10}$. So, 2k locations means $2 \times 2^{10}$ locations.
- Word Size: The second part, "16", represents the number of bits stored at each memory location. This is also known as the word size. When data is read from or written to memory, it is typically done in units of the word size.
Calculating Address Lines
To uniquely access each memory location, we need a certain number of address lines. If a memory unit has 'N' locations, the number of address lines required is given by $\log_2(N)$.
In our case, the number of locations is 2k. Let's convert 2k into a power of 2:
$\text{Number of locations} = 2 \times \text{1k} = 2 \times 2^{10} = 2^1 \times 2^{10} = 2^{(1+10)} = 2^{11}$
So, the memory has $2^{11}$ locations.
The number of address lines needed is $\log_2(2^{11})$. Using the logarithm property $\log_b(b^x) = x$, we get:
$\text{Number of address lines} = \log_2(2^{11}) = 11$
Therefore, 11 address lines are needed to access the $2^{11}$ memory locations.
Determining Input-Output Data Lines
The number of input-output data lines is determined by the word size of the memory unit. The word size tells us how many bits are stored at each location and how many bits are transferred in a single read or write operation.
The given memory unit is 2k × 16. The second number, 16, represents the word size in bits.
$\text{Word size} = 16 \text{ bits}$
This means that 16 bits of data are transferred into the memory during a write operation, and 16 bits of data are read out of the memory during a read operation. Thus, 16 input-output data lines are required.
Summary of Requirements
Based on the analysis:
- Number of Address Lines: 11
- Number of Input-Output Data Lines: 16
We can summarize the requirements in a table:
| Requirement | Value | Derivation |
|---|---|---|
| Memory Size | 2k × 16 bits | Given |
| Number of Locations | 2k = $2^{11}$ | $2 \times 2^{10}$ |
| Address Lines | 11 | $\log_2(2^{11})$ |
| Word Size | 16 bits | Given |
| Input-Output Data Lines | 16 | Matches Word Size |
Comparing these values with the given options, we find that 11 Address lines and 16 Data lines match one of the options.
Revision Table: Memory Address and Data Lines
| Memory Size (Locations × Word Size) | Number of Locations | Address Lines ($\log_2(\text{Locations})$) | Word Size | Data Lines |
|---|---|---|---|---|
| 1k × 8 | $1024 = 2^{10}$ | 10 | 8 bits | 8 |
| 4k × 16 | $4096 = 2^{12}$ | 12 | 16 bits | 16 |
| 64k × 32 | $65536 = 2^{16}$ | 16 | 32 bits | 32 |
| 2k × 16 | $2048 = 2^{11}$ | 11 | 16 bits | 16 |
Additional Information: Memory Addressing and Data Transfer
In a computer system, the CPU communicates with the memory unit to store and retrieve data. This communication happens through buses: the address bus, the data bus, and the control bus.
- Address Bus: This bus carries the address of the memory location that the CPU wants to access. The number of lines in the address bus determines the maximum number of memory locations that can be addressed. If there are 'A' address lines, the CPU can access $2^A$ locations.
- Data Bus: This bus carries the actual data being transferred between the CPU and memory. The width of the data bus (number of lines) is typically equal to the word size of the memory or the CPU's data processing capability, whichever is smaller or matched. In this case, the data lines are specified for the memory unit's word size.
- Control Bus: This bus carries control signals, such as read/write signals, memory enable, etc., to manage the memory operation.
For a memory unit of size 'M' locations × 'W' bits, you need $\log_2(M)$ address lines and W data lines.
In the 2k × 16 memory unit, 2k locations require 11 address lines, and the 16-bit word size requires 16 data lines for input and output.
Important Questions from Memory Management
Which of the following is the main function of the memory management system?
1. It keeps track of which parts of the memory are currently in use.
II. When memory is available, it allocates memory to the programs to be loaded.
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In light of the above statements, choose the correct answer from the options given below
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A. I/O Module
B. I/O processor
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