Megabytes per day to bits per second conversion

How to convert megabytes per day to bits per second?

To convert from megabytes per day (MB/day) to bits per second (bps), we need to follow a series of conversion steps. Note that there are two different definitions commonly used for megabytes: one based on base 10 and the other on base 2.

Conversion Steps:

1. Convert days to seconds:

   • 1 day = 24 hours
   • 1 hour = 60 minutes
   • 1 minute = 60 seconds $1 \text{ day} = 24 \times 60 \times 60 = 86,400 \text{ seconds}$

2. Convert megabytes to bits:

   • In base 10 (decimal), 1 megabyte (MB) = 1,000,000 bytes

   • In base 2 (binary), 1 megabyte (MiB) = 1,048,576 bytes

   • 1 byte = 8 bits

Base 10 Conversion (1 MB = 1,000,000 bytes)

1. Convert MB to bytes: $1 \text{ MB/day} = 1,000,000 \text{ bytes/day}$

2. Convert bytes to bits: $1,000,000 \text{ bytes/day} \times 8 \text{ bits/byte} = 8,000,000 \text{ bits/day}$

3. Convert bits per day to bits per second: $\frac{8,000,000 \text{ bits/day}}{86,400 \text{ seconds/day}} \approx 92.5926 \text{ bps}$

Base 2 Conversion (1 MiB = 1,048,576 bytes)

1. Convert MiB to bytes: $1 \text{ MiB/day} = 1,048,576 \text{ bytes/day}$

2. Convert bytes to bits: $1,048,576 \text{ bytes/day} \times 8 \text{ bits/byte} = 8,388,608 \text{ bits/day}$

3. Convert bits per day to bits per second: $\frac{8,388,608 \text{ bits/day}}{86,400 \text{ seconds/day}} \approx 97.136 \text{ bps}$

Real-World Examples:

1. Base 10: 100 MB/day

   • $100 \text{ MB/day}$
   • $100 \times 1,000,000 \times 8 = 800,000,000 \text{ bits/day}$
   • $\frac{800,000,000}{86,400} \approx 9260.278 \text{ bps}$

2. Base 2: 50 MiB/day

   • $50 \text{ MiB/day}$
   • $50 \times 1,048,576 \times 8 = 419,430,400 \text{ bits/day}$
   • $\frac{419,430,400}{86,400} \approx 4856.8 \text{ bps}$

3. Base 10: 1 GB/day

   • $1 \text{ GB/day} = 1,000 \text{ MB/day}$
   • $1,000 \times 1,000,000 \times 8 = 8,000,000,000 \text{ bits/day}$
   • $\frac{8,000,000,000}{86,400} \approx 92,592.6 \text{ bps}$

4. Base 2: 10 GiB/day

   • $10 \text{ GiB/day} = 10 \times 1,024 \text{ MiB/day}$
   • $10,240 \times 1,048,576 \times 8 = 85,899,345,920 \text{ bits/day}$
   • $\frac{85,899,345,920}{86,400} \approx 994,554.6 \text{ bps}$

These conversions might be useful in various scenarios, such as determining the network bandwidth required to handle a specific data load, or for comparing different storage and data transmission systems.