Bytes per second to Mebibytes per day conversion

How to convert bytes per second to mebibytes per day?

To convert Bytes per second (Bps) to Mebibytes per day, you need to consider both the time conversion (seconds to days) and the data unit conversion (Bytes to Mebibytes).

1. Time Conversion: Seconds to Days

   • There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.
   • So, the total number of seconds in a day is $60 \times 60 \times 24 = 86,400$ seconds.

2. Data Unit Conversion: Bytes to Mebibytes

   • In base 10 (decimal system), 1 Megabyte (MB) = 1,000,000 Bytes.
   • In base 2 (binary system), 1 Mebibyte (MiB) = 2$^ {20}$ Bytes = 1,048,576 Bytes.

Conversion Steps:

Base 10 (Decimal System):

1. Calculate total Bytes transferred in a day: $\text{Total Bytes} = 1 \text{ Bps} \times 86,400 \text{ seconds} = 86,400 \text{ Bytes}$
2. Convert Bytes to Megabytes: $\text{Total Megabytes} = \frac{86,400 \text{ Bytes}}{1,000,000 \text{ Bytes/MB}} = 0.0864 \text{ MB}$

Base 2 (Binary System):

1. Calculate total Bytes transferred in a day: $\text{Total Bytes} = 1 \text{ Bps} \times 86,400 \text{ seconds} = 86,400 \text{ Bytes}$
2. Convert Bytes to Mebibytes: $\text{Total Mebibytes} = \frac{86,400 \text{ Bytes}}{1,048,576 \text{ Bytes/MiB}} \approx 0.0824 \text{ MiB}$

Real-World Examples:

• Listening to an online radio stream: If the stream uses 128 Kbps (kilobits per second), which is equivalent to 16 KBps (kilobytes per second): $16 \text{ KBps} \times \frac{1,048,576 \text{ Bytes}}{1,000,000 \text{ KB}} = 16,777,216 \text{ Bytes}$ $16 \text{ KBps} = 16 \text{ KB} \times 86,400 \text{ sec/day} = 1,382,400 \text{ KB/day} \approx 1,360 \text{ MiB/day}$
• Downloading a 1GB file: If your internet speed is 10 MBps (Megabytes per second): $10 \text{ MBps} \times 3600 \text{ sec/hour} = 36,000 \text{ MB}$ $36,000 \text{ MB} \approx 35.16 \text{ GiB (Gibabytes)}$ So, downloading a 1GB file would take a few minutes at this rate.

Summary:

• In the base 10 system, 1 Byte per second is equivalent to 0.0864 MB per day.
• In the base 2 system, 1 Byte per second is equivalent to approximately 0.0824 MiB per day.

These conversions help in understanding how different data rates translate into practical usage over longer periods such as a day.