How much memory is required to store a black and white image that is 10 pixels high and 5 pixels wide?
Understand the Problem
The question is asking us to calculate the amount of memory needed to store a black and white image based on its dimensions. Since the image is black and white, each pixel will typically require 1 bit of memory. The total memory requirement can be calculated by multiplying the dimensions of the image (height and width).
Answer
The memory needed to store the image is $60,000$ bytes.
Answer for screen readers
The memory needed to store the image is $60,000$ bytes for the example dimensions (800 pixels x 600 pixels).
Steps to Solve
- Identify the dimensions of the image
Determine the width and height of the image in pixels. For example, let’s say the image dimensions are 800 pixels wide and 600 pixels high.
- Calculate the total number of pixels
Multiply the width and height to find the total number of pixels in the image.
$$ \text{Total Pixels} = \text{Width} \times \text{Height} $$
For our example: $$ \text{Total Pixels} = 800 \times 600 $$
- Calculate the memory requirement in bits
Since it's a black and white image, each pixel requires 1 bit. So, the memory in bits is equal to the total number of pixels calculated in the previous step.
$$ \text{Memory (in bits)} = \text{Total Pixels} $$
- Convert memory requirement to bytes
Since there are 8 bits in a byte, divide the total memory in bits by 8 to convert it to bytes.
$$ \text{Memory (in bytes)} = \frac{\text{Memory (in bits)}}{8} $$
- Final Calculation
Plug in the values to get the final memory requirement in bytes.
The memory needed to store the image is $60,000$ bytes for the example dimensions (800 pixels x 600 pixels).
More Information
For a black and white image, storing the memory calculation in bits and converting it to bytes gives you a straightforward way to understand how much storage is required. Knowing this is particularly helpful in fields like computer graphics and web design where file sizes are crucial.
Tips
- Forgetting to convert bits to bytes after calculating the total bit memory.
- Incorrectly multiplying width and height due to misreading the dimensions.
