Question

Suppose a digital camera has a storage capacity of \(500 \mathrm{MB}\). How many blackand-white photographs could be stored in the camera if each consisted of 512 pixels per row and 512 pixels per column if each pixel required one bit of storage?

Short answer

Approximately 16,000 black-and-white photographs can be stored.

Step-by-step solution

Determine the Total Number of Pixels Per Photograph

Given that each photograph is 512 pixels per row and 512 pixels per column, calculate the total number of pixels using the formula: \[ 512 \times 512 = 262,144 \text{ pixels} \] This is how many pixels are in each photograph.

Determine the Storage Requirement Per Photograph

Since each pixel requires one bit of storage, the total storage required for one photograph is equal to the number of pixels, which is 262,144 bits per photograph.

Convert Megabytes to Bits

The camera's storage capacity is given as 500 megabytes. We need to convert this capacity to bits for consistency in units. Recall:\[ 1 \text{ byte} = 8 \text{ bits} \]\[ 1 \text{ megabyte} = 1,024 \times 1,024 \text{ bytes} \]Thus:\[ 500 \text{ MB} = 500 \times 1,024 \times 1,024 \times 8 \text{ bits} = 4,194,304,000 \text{ bits} \]

Calculate the Number of Photographs That Can Be Stored

Using the total storage capacity in bits, divide by the number of bits required per photograph:\[ \frac{4,194,304,000 \text{ bits}}{262,144 \text{ bits per photograph}} \approx 16,000 \]Thus, approximately 16,000 photographs can be stored.

Key concepts

Digital Photography

Digital photography has transformed the traditional art of capturing images. Unlike film cameras that use photographic films, digital cameras capture images electronically. When you press the shutter on a digital camera, it captures the view through the lens as an array of pixels, each representing a tiny part of the scene. In our example, each photograph consists of 512 pixels per row and 512 pixels per column, creating a grid we call a resolution. This particular resolution forms a total of 262,144 pixels per image.

These images are stored as digital files on memory cards. Each pixel captures a bit of data, which is why understanding digital data storage is crucial for digital photography. With advancements in technology, even small devices can store thousands of images, enabling both amateur photographers and professionals to shoot moments countless times.

Bits and Bytes

When discussing digital data, 'bits' and 'bytes' are fundamental units of measurement. A 'bit' is the smallest unit of data in a computer and can have a value of either 0 or 1. It represents a binary state. In our photography exercise, each pixel requires one bit of storage to represent the captured data.

Meanwhile, a 'byte' consists of 8 bits. This means for larger data representations, bytes become very useful. For instance, when referring to storage capacity, we use bytes. Files, like photographs in digital form, are described with bytes because they contain far more than just a few bits of data. Understanding these conversions from bits to bytes is necessary for calculating digital storage requirements.

• 1 Byte = 8 Bits
• 1 Kilobyte (KB) = 1,024 Bytes
• 1 Megabyte (MB) = 1,024 KB

Storage Capacity in Megabytes

Digital storage capacity is often measured in megabytes (MB), which translates to 1,024 kilobytes or 1,024 squared bytes. For photographers, memory or storage capacity is vital because it determines how many photographs they can store and access at any time. In the given exercise, a digital camera has a storage capacity of 500 MB.

To find out how many photographs can be stored, it requires calculation from megabytes down to bits. We know 1 MB is equivalent to 1,024 × 1,024 bytes, and each byte is 8 bits. Hence, 500 MB equals 4,194,304,000 bits. Calculating the storage requirement per photograph, which we found to be 262,144 bits, we can divide the total storage capacity by this number to determine that approximately 16,000 photographs can be stored on the camera.

• 1 MB = 1,024 x 1,024 Bytes
• Total Storage Capacity in Bits = 500 MB × 8 Bits per Byte
• Number of Photographs = Total Bits ÷ Bits per Photograph