A file is downloaded to a home computer using a 56 kbps modem connected to an Internet Service Provider. If the download completes in 2 minutes, estimate the maximum size of data d... A file is downloaded to a home computer using a 56 kbps modem connected to an Internet Service Provider. If the download completes in 2 minutes, estimate the maximum size of data downloaded.
Understand the Problem
The question is asking to calculate the maximum size of data that can be downloaded with a given modem speed and download duration. We will use the modem speed, the time taken for the download, and the appropriate unit conversions to find the total size of data downloaded.
Answer
The maximum size of data downloaded is approximately 840 kilobytes, or about 0.828 megabytes.
Answer for screen readers
The maximum size of data downloaded is approximately 840 kilobytes, or about 0.828 megabytes.
Steps to Solve
- Identify modem speed and duration
The modem speed is given as 56 kbps (kilobits per second), and the download duration is 2 minutes.
- Convert download duration to seconds
Since the speed is in seconds, convert 2 minutes to seconds: $$ 2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds} $$
- Calculate total number of bits downloaded
Use the formula to calculate the total bits downloaded: $$ \text{Total bits} = \text{speed} \times \text{time} $$ Substituting in the values: $$ \text{Total bits} = 56 \text{ kbps} \times 120 \text{ seconds} = 6720 \text{ kilobits} $$
- Convert bits to bytes
To convert kilobits to bytes, use the conversion factor (1 \text{ byte} = 8 \text{ bits}): $$ \text{Total bytes} = \frac{6720 \text{ kilobits}}{8} = 840 \text{ kilobytes} $$
- Convert kilobytes to megabytes (optional)
If needed, convert kilobytes to megabytes using the conversion (1 \text{ MB} = 1024 \text{ KB}): $$ \text{Total MB} = \frac{840 \text{ KB}}{1024} \approx 0.828 \text{ MB} $$
The maximum size of data downloaded is approximately 840 kilobytes, or about 0.828 megabytes.
More Information
This calculation shows the relationship between modem speed, time, and the size of data transferred. Understanding bits and bytes is essential in data communication, as these units help evaluate download capabilities.
Tips
- Confusing bits with bytes: Remember that 1 byte = 8 bits. This is critical when converting between units.
- Neglecting to convert time into the correct unit (seconds) before performing calculations.
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