Gibibytes per hour to Terabits per hour conversion

How to convert gibibytes per hour to terabits per hour?

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Conversion: Gibibytes per Hour to Terabits per Hour

Step 1: Understand the Units

1 Gibibyte (GiB) is equal to $2^{30}$ bytes or 1,073,741,824 bytes (base 2). 1 terabit (Tb) is equal to $10^{12}$ bits (base 10) or $2^{40}$ bits (base 2).

Step 2: Conversion in Base 2

1 GiB = $2^{30}$ bytes = $2^{33}$ bits (since 1 byte = 8 bits)

Thus, 1 GiB/hour = $2^{33}$ bits/hour

To convert this to terabits per hour (base 2): 1 Tb (base 2) = $2^{40}$ bits

So, $\text{Terabits per hour (base 2)} = \frac{2^{33} \text{ bits/hour}}{2^{40} \text{ bits/Tb}} = 2^{33-40} \text{ Tb/hour} = 2^{-7} \text{ Tb/hour} = \frac{1}{128} \text{ Tb/hour} \approx 0.0078125 \text{ Tb/hour}$

Step 3: Conversion in Base 10

For base 10, 1 GiB = 1,073,741,824 bytes = 1,073,741,824 * 8 bits = 8,589,934,592 bits

1 terabit (Tb) = $10^{12}$ bits

Thus, $\text{Terabits per hour (base 10)} = \frac{8,589,934,592 \text{ bits/hour}}{10^{12} \text{ bits/Tb}} = \frac{8,589,934,592}{1,000,000,000,000} \text{ Tb/hour} \approx 0.00858993 \text{ Tb/hour}$

Real-World Examples

1. Consumer Internet Plans: An internet plan might offer download speeds of 300 Megabits per second (Mbps).

   Converting this to GiB/hour: 300 Mbps = 300 * $10^6$ bits/second = 37.5 Megabytes per second (MBps) = 37.5 * 3600 seconds/hour = 135,000 MB/hour = 131.8359375 GiB/hour (base 2).

2. Data Centers: A data center might transfer data to a backup location at a rate of 2 Gibibytes per hour.

   Converting 2 GiB/hour to Tb/hour: For base 2: $2 \times 0.0078125 \text{ Tb/hour} = 0.015625 \text{ Tb/hour}$ For base 10: $2 \times 0.00858993 \text{ Tb/hour} \approx 0.01717986 \text{ Tb/hour}$

3. Large File Transfers: Suppose you're transferring a large dataset of 50 GiB from a server to local storage over a network running at 10 Gibibytes per hour.

   Conversions: For base 2: $10 \times 0.0078125 \text{ Tb/hour} = 0.078125 \text{ Tb/hour}$ For base 10: $10 \times 0.00858993 \text{ Tb/hour} \approx 0.0858993 \text{ Tb/hour}$

I hope this breakdown of the conversion process and real-world examples helps you understand how to convert Gibibytes per hour to Terabits per hour.