Megabits per hour to Tebibytes per day conversion

How to convert megabits per hour to tebibytes per day?

Converting 1 Megabit per Hour (Mb/h) to Tebibytes per Day (TiB/day) involves several steps, mainly converting units of time and data storage. The answer indeed has differences when using base 10 (decimal) versus base 2 (binary) measurements. Let's break this down step by step.

Conversion Factors

1. Time Conversion:

   • Hours to Days: There are 24 hours in a day.

2. Data Storage Conversion:

   • Base 10 (Decimal): 1 Megabit (Mb) = 1,000,000 bits.

   • Base 2 (Binary): 1 Megabit (Mb) = 1024 Kibibits (Kib) = 1024 * 1024 bits.

   • Base 10 (Decimal): 1 Tebibyte (TiB) = 10^12 bytes

   • Base 2 (Binary): 1 Tebibyte (TiB) = 1024^4 bytes

3. Time-Related Data Rate:

   • Mb/h to Mb/day: Multiply by 24 (since there are 24 hours in a day).

Conversion Steps

Step 1: Convert Mb/h to Mb/day

$1 \text{ Mb/h} \times 24 \text{ hours/day} = 24 \text{ Mb/day}$

Step 2: Convert Mb/day to bits/day

• In Base 10: $24 \text{ Mb/day} = 24 \times 1,000,000 \text{ bits/day} = 24,000,000 \text{ bits/day}$

• In Base 2: $24 \text{ Mb/day} = 24 \times 1024 \times 1024 \text{ bits/day} = 24 \times 1,048,576 \text{ bits/day} = 25,165,824 \text{ bits/day}$

Step 3: Convert bits/day to Tebibytes/day

• In Base 10: $24,000,000 \text{ bits/day} \div (8 \times 10^{12}) \text{ bits/TiB} = 3 \times 10^{-6} \text{ TiB/day} = 0.000003 \text{ TiB/day}$

• In Base 2: $25,165,824 \text{ bits/day} \div (8 \times 1024^4) \text{ bits/TiB} = 25,165,824 \div 8,796,093,022,208 = 2.862 \times 10^{-6} \text{ TiB/day}$

Summary of Conversions

• Base 10: 1 Megabit per Hour = 0.000003 Tebibytes per Day.
• Base 2: 1 Megabit per Hour = 0.000002862 Tebibytes per Day.

Real-World Examples

Let's examine a few other example quantities of data transfer rates in Megabits per hour:

1. 5 Mb/h:

   • To TiB/day (Base 10): $5 \times 24 \text{ Mb/day} = 120 \text{ Mb/day}$ $120 \times 1,000,000 \text{ bits/day} = 120,000,000 \text{ bits/day}$ $= 120,000,000 \text{ bits/day} \div 8,000,000,000,000 \text{ bits/TiB} = 0.000015 \text{ TiB/day}$

   • To TiB/day (Base 2): $5 \times 25,165,824 \text{ bits/day} = 125,829,120 \text{ bits/day}$ $= 125,829,120 \div 8,796,093,022,208 = 0.00001435 \text{ TiB/day}$

2. 100 Mb/h:

   • To TiB/day (Base 10): $100 \times 24 \text{ Mb/day} = 2400 \text{ Mb/day}$ $2400 \times 1,000,000 \text{ bits/day} = 2,400,000,000 \text{ bits/day}$ $= 2,400,000,000 \div 8,000,000,000,000 \text{ bits/TiB} = 0.0003 \text{ TiB/day}$

   • To TiB/day (Base 2): $100 \times 25,165,824 \text{ bits/day} = 2,516,582,400 \text{ bits/day}$ $= 2,516,582,400 \div 8,796,093,022,208 = 0.000286 \text{ TiB/day}$

By understanding these conversions, you can better grasp how data transfer rates correspond to large data storage units over extended periods of time.