A digital camera contains a microprocessor. The camera's specification includes : 20 megapixel resolution 32 gigabyte memory card autofocus facility If a compressed image file requires an average of 1 byte per pixel, then what is the maximum number of photos that can be stored on the memory card? (1 Kilo = 1024)
Calculating Digital Camera Photo Storage
This question asks us to determine the maximum number of compressed photos that can be stored on a digital camera's memory card, based on its resolution and the average file size per pixel.
Understanding the Given Information
- Camera Resolution: 20 megapixels
- Memory Card Capacity: 32 gigabytes
- Average Compressed Image File Size: 1 byte per pixel
- Conversion factor: 1 Kilo = 1024
We need to calculate the total size of one photo in bytes and the total capacity of the memory card in bytes using the given conversion factor where 1 Kilo = 1024. Then, we can divide the total memory capacity by the size of one photo to find the number of photos that can be stored.
Step 1: Calculate the size of one photo in bytes
The resolution is 20 megapixels. Using the conversion 1 Kilo = 1024, we interpret 'Mega' as 1024 multiplied by 1024 (since Mega is Kilo * Kilo).
- 1 megapixel \( = 1024 \times 1024 \) pixels
- 20 megapixels \( = 20 \times 1024 \times 1024 \) pixels
Each pixel requires 1 byte for a compressed image.
Size of one photo \( = \) Number of pixels \( \times \) Bytes per pixel
Size of one photo \( = 20 \times 1024 \times 1024 \times 1 \) bytes
Size of one photo \( = 20 \times 1048576 \) bytes
Size of one photo \( = 20971520 \) bytes
Step 2: Calculate the total capacity of the memory card in bytes
The memory card capacity is 32 gigabytes. Using the conversion 1 Kilo = 1024, we convert Gigabytes to bytes:
- 1 Gigabyte (GB) \( = 1024 \) Megabytes (MB)
- 1 Megabyte (MB) \( = 1024 \) Kilobytes (KB)
- 1 Kilobyte (KB) \( = 1024 \) bytes
- So, 1 Gigabyte \( = 1024 \times 1024 \times 1024 \) bytes
Total memory card capacity \( = 32 \times 1024 \times 1024 \times 1024 \) bytes
Total memory card capacity \( = 32 \times 1073741824 \) bytes
Total memory card capacity \( = 34359738368 \) bytes
Step 3: Calculate the maximum number of photos
To find the maximum number of photos, divide the total memory card capacity by the size of one photo.
Maximum number of photos \( = \frac{\text{Total memory card capacity}}{\text{Size of one photo}} \)
Maximum number of photos \( = \frac{32 \times 1024 \times 1024 \times 1024}{20 \times 1024 \times 1024} \)
We can simplify this calculation by cancelling out the \( 1024 \times 1024 \) terms:
Maximum number of photos \( = \frac{32 \times 1024}{20} \)
Maximum number of photos \( = \frac{32768}{20} \)
Maximum number of photos \( = 1638.4 \)
Since you cannot store a fraction of a photo, the maximum number of complete photos that can be stored is the integer part of the result.
Maximum number of photos \( = 1638 \)
Therefore, the maximum number of photos that can be stored on the 32 gigabyte memory card is 1638.
| Calculation Step | Formula / Value | Result (Bytes) |
|---|---|---|
| Pixels per Megapixel (using Kilo=1024) | \(1024 \times 1024\) | 1048576 |
| Size of one photo (20 MP) | \(20 \times 1024 \times 1024\) | 20971520 |
| Bytes per Gigabyte (using Kilo=1024) | \(1024 \times 1024 \times 1024\) | 1073741824 |
| Total Memory Capacity (32 GB) | \(32 \times 1024 \times 1024 \times 1024\) | 34359738368 |
| Maximum Photos | \((32 \times 1024 \times 1024 \times 1024) / (20 \times 1024 \times 1024)\) | 1638.4 |
| Maximum whole Photos | Integer part of 1638.4 | 1638 |
Revision Table: Key Concepts for Digital Camera Storage
| Term | Definition | Relevance to Question |
|---|---|---|
| Megapixel (MP) | One million pixels. In computing and digital imaging, often \(1024 \times 1024\) pixels. | Defines the resolution and thus the base size of an image. |
| Byte | A unit of digital information, typically 8 bits. | The fundamental unit for measuring file size and storage capacity. |
| Gigabyte (GB) | One billion bytes. In computing (using 1024 base), often \(1024 \times 1024 \times 1024\) bytes. | Measures the total capacity of the memory card. |
| Pixel | The smallest individual unit of a digital image or graphic display that can be represented. | The building block of the image, and its size contributes to the total file size. |
Additional Information: Digital Imaging Storage
When dealing with digital camera storage, several factors influence how many photos you can store:
- Resolution: Higher resolution (more megapixels) means more pixels, leading to larger file sizes if other factors remain constant.
- File Format and Compression: Different formats like JPEG, TIFF, and RAW have different file sizes. JPEG uses compression, reducing file size significantly, though quality might be slightly affected. TIFF and RAW formats are typically much larger but retain more image data. The question specifies a "compressed image file" with an average of 1 byte per pixel, which is a highly compressed scenario compared to uncompressed formats that might use 3 bytes per pixel (for RGB color).
- Color Depth: This refers to the number of bits used to represent the color of a single pixel. A higher color depth allows for more colors but increases file size. For example, an uncompressed 24-bit RGB image uses 3 bytes per pixel.
- Decimal vs. Binary Prefixes: Manufacturers sometimes use decimal prefixes (Kilo=1000, Mega=10002, Giga=10003) for storage capacity, while operating systems and file systems often use binary prefixes (Kibi=1024, Mebi=10242, Gibi=10243). The question explicitly states "1 Kilo = 1024", indicating the use of binary prefixes for this calculation. This is crucial for getting the correct numerical answer.
Understanding these concepts helps in estimating storage needs and managing photos on digital devices.
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