Problem 51 - Computer Science: An Overview

Question

Suppose a machine has 200 GB of storage space available on a hard disk and receives data over a broadband connection at the rate of \(15 \mathrm{Mbps}\). At this rate, how long will it take to fill the available storage space?

Step-by-Step Solution

Answer

It will take approximately 30.34 hours to fill the storage.

Step 1: Convert Data Storage to Megabits

First, we need to convert the available storage space from gigabytes (GB) to megabits (Mb) in order to match the broadband speed's units. We know that 1 byte equals 8 bits and 1 GB equals 1024 megabytes (MB). Therefore, 1 GB equals 1024 MB * 8 bits (because there are 8 bits in a byte) = 8192 megabits.Thus, 200 GB = \( 200 \times 8192 \) megabits = \( 1,638,400 \) megabits.

Step 2: Determine Time to Fill Storage

Now, we calculate the time needed to fill the storage. We divide the total storage in megabits by the data transfer rate to find out how many seconds it would take.The time in seconds is given by \( \frac{1,638,400 \text{ Mb}}{15 \text{ Mbps}} = 109,226.67 \text{ seconds} \).

Step 3: Convert Seconds to Hours

Convert the time from seconds to hours by dividing by the number of seconds in an hour (3600 seconds per hour).\( \frac{109,226.67 \text{ seconds}}{3600 \text{ seconds/hour}} \approx 30.34 \text{ hours} \).

Key Concepts

Storage Capacity

Understanding storage capacity is essential in computing and data management. It represents the maximum amount of data that a storage device can hold.
Storage capacity is often measured in multiple units to accommodate various sizes of data. Here are common units of measurement:

• Byte (B): It is the basic unit of storage used in computing, consisting of 8 bits.
• Kilobyte (KB): Equivalent to 1024 bytes.
• Megabyte (MB): Consists of 1024 kilobytes.
• Gigabyte (GB): Equals 1024 megabytes. A gigabyte is suitable for measuring larger amounts of data like files and software.
• Terabyte (TB): Equal to 1024 gigabytes, often used for assessing hard drive capacities.

For this specific problem, the storage capacity is given as 200 GB. To find how long it will take to fill, we need uniform units, compatible with the data transfer rate.

Broadband Speed

Broadband speed indicates how fast data can be downloaded or uploaded. It is expressed in bits per second, commonly megabits per second (Mbps).
This exercise uses a broadband speed of 15 Mbps, denoting the ability to transfer 15 million bits per second.

• Bits vs. Bytes: Networks use bits (b), while storage is usually in bytes (B). Recall that 1 byte equals 8 bits.
• Speed Consistency: Actual broadband speeds may vary due to network traffic and other factors.

Understanding data transfer speeds in terms of bits per second helps ensure that calculations are accurate and reflect realistic timelines for data processes.

Unit Conversion

When working in computing, converting between different units of measurement is fundamental. Proper unit conversion provides uniformity, enabling accurate calculations.

• Gigabytes to Megabits: This conversion is vital in this scenario. Convert gigabytes (GB) to megabits (Mb) by multiplying the gigabytes by 8192 (since 1 GB = 1024 MB and 1 MB = 8 Mb). When converted, 200 GB becomes 1,638,400 Mb.
• Consistency Across Units: Ensures compatibility with the broadband speed unit of Megabits per second. It standardizes the data sizes for correct computational processing.

This conversion process might at first seem complex, but, with practice, it becomes a straightforward part of handling data.

Time Calculation

Time calculation is crucial for determining how long a given process, like data transfer, will take. It involves calculating durations based on transfer rates and total data quantities.
In this problem, after converting storage to megabits, we divide it by the broadband speed:

• Calculate Time in Seconds: Total storage (1,638,400 Mb) divided by transfer speed (15 Mbps) gives 109,226.67 seconds.
• Convert to Readable Units: Converting seconds into hours makes it more relatable. Divide by 3600 seconds/hour to obtain 30.34 hours.

Understanding time calculations helps in planning data transfers effectively, estimating resource usage, and managing time efficiently.