bits per second to Megabytes per day conversion

How to convert bits per second to megabytes per day?

To convert bits per second (bps) to Megabytes per day (MB/day), you need to understand the relationship between bits, bytes, seconds, and days. The calculation will differ slightly depending on whether you use the decimal (base 10) or binary (base 2) system for data units.

Base 10 (Decimal System)

1. Convert bits per second to bits per day:

   • There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.
   • Therefore, there are $60 \times 60 \times 24 = 86,400$ seconds in a day.
   • For 1 bit per second: $\text{bits per day} = 1 \, \text{bit/second} \times 86,400 \, \text{seconds/day} = 86,400 \, \text{bits/day}$

2. Convert bits to bytes:

   • There are 8 bits in 1 byte.
   • So: $\text{bytes per day} = \frac{86,400 \, \text{bits/day}}{8 \, \text{bits/byte}} = 10,800 \, \text{bytes/day}$

3. Convert bytes to Megabytes using base 10 (1 MB = 1,000,000 bytes):

   • $\text{Megabytes per day} = \frac{10,800 \, \text{bytes/day}}{1,000,000 \, \text{bytes/MB}} = 0.0108 \, \text{MB/day}$

Base 2 (Binary System)

1. Convert bits per second to bits per day:

   • The number of seconds per day remains the same, $86,400$.

2. Convert bits to bytes:

   • Still, there are 8 bits in 1 byte.
   • $\text{bytes per day} = \frac{86,400 \, \text{bits/day}}{8 \, \text{bits/byte}} = 10,800 \, \text{bytes/day}$

3. Convert bytes to Megabytes using base 2 (1 MiB = 1,048,576 bytes):

   • $\text{Megabytes per day} = \frac{10,800 \, \text{bytes/day}}{1,048,576 \, \text{bytes/MiB}} \approx 0.0103 \, \text{MiB/day}$

Summary:

• Base 10 (Decimal System): 1 bit per second equals 0.0108 MB/day.
• Base 2 (Binary System): 1 bit per second equals approximately 0.0103 MiB/day.

Real World Examples:

1. Low-speed IoT Device:

   • Assume a simple IoT sensor transmits data at 100 bps.
   • In base 10: $100 \, \text{bps} \times 0.0108 \, \frac{\text{MB}}{\text{bps day}} = 1.08 \, \text{MB/day}$
   • In base 2: $100 \, \text{bps} \times 0.0103 \, \frac{\text{MiB}}{\text{bps day}} = 1.03 \, \text{MiB/day}$

2. Standard Home Network Speed:

   • Assume an internet download speed of 100 Mbps.
   • In base 10: $100 \, \text{Mbps} \times \frac{86,400 \times 10^6 \, \text{bits/day}}{8 \times 10^6 \, \text{bytes/MB}} = 10,800 \, \text{MB/day}$
   • In base 2: $100 \, \text{Mbps} \times \frac{86,400 \times 10^6 \, \text{bits/day}}{8 \times 1,048,576 \, \text{bytes/MiB}} \approx 10,240 \, \text{MiB/day}$

3. 5G Network Connection:

   • Assume a high-speed 5G network offering 1 Gbps.
   • In base 10: $1,000 \, \text{Mbps} \times 0.0108 = 10,800 \, \text{GB/day}$
   • In base 2: $1,000 \, \text{Mbps} \times 0.0103 = 10,240 \, \text{GiB/day}$

These calculations help illustrate how different data rates convert into daily transfers in both base 10 and base 2 formats.