Bytes per day to Megabits per hour conversion

How to convert bytes per day to megabits per hour?

To convert 1 Byte per day to Megabits per hour, you'll need to follow a series of unit conversions. Let's break it down step by step, considering both the base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal)

1 byte = 8 bits (This is true for both base 10 and base 2)

1 day = 24 hours

To find the number of bits per day: $1 \text{ Byte/day} \times 8 \text{ bits/Byte} = 8 \text{ bits/day}$

To convert from bits per day to bits per hour: $8 \text{ bits/day} \div 24 \text{ hours/day} = \frac{8}{24} \text{ bits/hour} = \frac{1}{3} \text{ bits/hour} \approx 0.3333 \text{ bits/hour}$

Now, convert bits per hour to Megabits per hour (using base 10): 1 Megabit (Mb) = 1,000,000 bits

$0.3333 \text{ bits/hour} \div 1,000,000 \text{ bits/Mb} = 0.0000003333 \text{ Mb/hour}$

So, in base 10: $1 \text{ Byte/day} \approx 0.0000003333 \text{ Megabits/hour}$

Base 2 (Binary)

1 byte = 8 bits (Again, this is true for both base 10 and base 2)

1 day = 24 hours

Using the same initial conversions as before: $1 \text{ Byte/day} \times 8 \text{ bits/Byte} = 8 \text{ bits/day}$

To convert from bits per day to bits per hour: $8 \text{ bits/day} \div 24 \text{ hours/day} = \frac{8}{24} \text{ bits/hour} = \frac{1}{3} \text{ bits/hour} \approx 0.3333 \text{ bits/hour}$

In base 2, 1 Megabit (Mib) = 2^20 bits = 1,048,576 bits

$0.3333 \text{ bits/hour} \div 1,048,576 \text{ bits/Mib} = 0.0000003188 \text{ Mib/hour}$

So, in base 2: $1 \text{ Byte/day} \approx 0.0000003188 \text{ Mib/hour}$

Real-World Examples for Various Quantities of Bytes per Day

1. 50 GB/day (Base 10):

   • Convert to Bytes: $50 \times 10^9$ Bytes
   • Bytes to Bits: $50 \times 10^9 \times 8$
   • Bits per hour: $\frac{50 \times 10^9 \times 8}{24}$
   • Megabits per hour (Base 10): $\frac{50 \times 10^9 \times 8}{24 \times 10^6} \approx 16,666.67$ Mb/hour

2. 1 TB/day (Base 10):

   • Convert to Bytes: $1 \times 10^{12}$ Bytes
   • Bytes to Bits: $1 \times 10^{12} \times 8$
   • Bits per hour: $\frac{1 \times 10^{12} \times 8}{24}$
   • Megabits per hour (Base 10): $\frac{1 \times 10^{12} \times 8}{24 \times 10^6} \approx 333,333.33$ Mb/hour

3. 5 MB/day (Base 10):

   • Convert to Bytes: $5 \times 10^6$ Bytes
   • Bytes to Bits: $5 \times 10^6 \times 8$
   • Bits per hour: $\frac{5 \times 10^6 \times 8}{24}$
   • Megabits per hour (Base 10): $\frac{5 \times 10^6 \times 8}{24 \times 10^6} \approx 1.6667$ Mb/hour

By following these steps, you can convert any given data rate from Bytes per day to Megabits per hour in both base 10 and base 2.