bits per second to Mebibytes per day conversion

How to convert bits per second to mebibytes per day?

To convert 1 bit per second (bps) to mebibytes per day (MiB/day), you need to know the following:

1. There are 86,400 seconds in a day (24 hours * 60 minutes * 60 seconds).
2. A mebibyte (MiB) is $2^{20}$ or 1,048,576 bytes.
3. Each byte consists of 8 bits.

Using Base 2 (Binary - IEC Standard)

Here's the detailed calculation step-by-step:

Step 1: Convert bits per second to bits per day: $1 \text{ bit/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$

Step 2: Convert bits to bytes (since there are 8 bits in a byte): $\frac{86,400 \text{ bits/day}}{8 \text{ bits/byte}} = 10,800 \text{ bytes/day}$

Step 3: Convert bytes to mebibytes (since 1 MiB = 1,048,576 bytes): $\frac{10,800 \text{ bytes/day}}{1,048,576 \text{ bytes/MiB}} \approx 0.0103 \text{ MiB/day}$

Using Base 10 (Decimal - SI Standard)

In the decimal (SI) system:

1. 1 byte = 8 bits
2. 1 megabyte (MB) = 1,000,000 bytes (note that this does not strictly pertain to mebibytes but to understand the difference)

Step 1: Convert bits per second to bits per day: $1 \text{ bit/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$

Step 2: Convert bits to bytes: $\frac{86,400 \text{ bits}}{8 \text{ bits/byte}} = 10,800 \text{ bytes/day}$

Step 3: Convert bytes to megabytes (in the decimal system): $\frac{10,800 \text{ bytes}}{1,000,000 \text{ bytes/MB}} = 0.0108 \text{ MB/day}$

Recap of Conversions

• Base 2 (Binary - IEC Standard): $1 \text{ bit/second} = 0.0103 \text{ MiB/day}$

• Base 10 (Decimal - SI Standard): $1 \text{ bit/second} = 0.0108 \text{ MB/day}$

Real-World Examples for Other Quantities of Bits per Second

1. 56 kbps (Dial-up Internet Connection):

   • Base 2: $56,000 \text{ bps} \rightarrow 486 MiB/day$
   • Base 10: $56,000 \text{ bps} \rightarrow 483.84 MB/day$

2. 10 Mbps (Home Broadband):

   • Base 2: $10,000,000 \text{ bps} \rightarrow 1098.64 MiB/day$
   • Base 10: $10,000,000 \text{ bps} \rightarrow 1080 MB/day$

3. 1 Gbps (Fiber Optic Connection):

   • Base 2: $1,000,000,000 \text{ bps} \rightarrow 1098616 MiB/day$
   • Base 10: $1,000,000,000 \text{ bps} \rightarrow 1080000 MB/day$

These conversions help show the difference between binary and decimal measurements and illustrate how varying internet speeds translate to daily data throughput.