bits per day to Mebibytes per day conversion

How to convert bits per day to mebibytes per day?

Certainly! To convert bits per day to Mebibytes per day, we need to understand the relationships between the units involved.

First, let's break down the steps needed for the conversion:

1. Bits to Bytes: There are 8 bits in 1 byte.

2. Bytes to Megabytes (MB) or Mebibytes (MiB):

   • In base 10 (decimal), 1 Megabyte (MB) is $10^6$ bytes (1,000,000 bytes).
   • In base 2 (binary), 1 Mebibyte (MiB) is $2^{20}$ bytes (1,048,576 bytes).

Converting 1 bit per day to Mebibytes per day

Base 10 (Decimal) Conversion:

1. Start with 1 bit per day.
2. Convert bits to bytes:
   • $1 \text{ bit} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 0.125 \text{ bytes}$
3. Convert bytes to Megabytes (MB):
   • $0.125 \text{ bytes} \times \frac{1 \text{ MB}}{1,000,000 \text{ bytes}} = 0.125 \times 10^{-6} \text{ MB} = 1.25 \times 10^{-7} \text{ MB}$

1 bit per day is $1.25 \times 10^{-7}$ Megabytes per day in base 10.

Base 2 (Binary) Conversion:

1. Start with 1 bit per day.
2. Convert bits to bytes:
   • $1 \text{ bit} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 0.125 \text{ bytes}$
3. Convert bytes to Mebibytes (MiB):
   • $0.125 \text{ bytes} \times \frac{1 \text{ MiB}}{1,048,576 \text{ bytes}} = 0.125 \div 1,048,576 \text{ MiB} = 1.192 \times 10^{-7} \text{ MiB}$

1 bit per day is $1.192 \times 10^{-7}$ Mebibytes per day in base 2.

Real-World Examples for Other Quantities of Bits per Day

1. 1 Kbps (kilobit per second):

   • Bits per day:
     • $1 \text{ Kbps} \times 1000 \text{ bits} \times 60 \text{ seconds/min} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400,000 \text{ bits/day}$
   • Base 10:
     • $86,400,000 \text{ bits/day} \div 8 = 10,800,000 \text{ bytes/day} \div 1,000,000 = 10.8 \text{ MB/day}$
   • Base 2:
     • $10,800,000 \text{ bytes/day} \div 1,048,576 = 10.3 \text{ MiB/day}$

2. 1 Mbps (megabit per second):

   • Bits per day:
     • $1 \text{ Mbps} \times 1,000,000 \text{ bits} \times 60 \text{ seconds/min} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400,000,000 \text{ bits/day}$
   • Base 10:
     • $86,400,000,000 \text{ bits/day} \div 8 = 10,800,000,000 \text{ bytes/day} \div 1,000,000 = 10,800 \text{ MB/day}$
   • Base 2:
     • $10,800,000,000 \text{ bytes/day} \div 1,048,576 = 10,302.4 \text{ MiB/day}$

3. 1 Gbps (gigabit per second):

   • Bits per day:
     • $1 \text{ Gbps} \times 1,000,000,000 \text{ bits} \times 60 \text{ seconds/min} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400,000,000,000 \text{ bits/day}$
   • Base 10:
     • $86,400,000,000,000 \text{ bits/day} \div 8 = 10,800,000,000,000 \text{ bytes/day} \div 1,000,000 = 10,800,000 \text{ MB/day}$
   • Base 2:
     • $10,800,000,000,000 \text{ bytes/day} \div 1,048,576 = 10,302,400 \text{ MiB/day}$

These examples show how the data rate can scale significantly depending on the bit rate, and how the conversion between different units of measurement leads to sizable differences depending on whether a base 10 or base 2 system is used.