Tebibits per day to Gigabytes per hour conversion

How to convert tebibits per day to gigabytes per hour?

Sure, I'd be happy to explain how to convert Tebibits per day to Gigabytes per hour, including both base 10 (decimal) and base 2 (binary) answers. Then, I'll provide some real-world examples for other quantities of Tebibits per day.

Conversion Concept

1 Tebibit (Tib) = 2^40 bits (in base 2) 1 Gigabyte (GB) = 10^9 bytes (in base 10) or 2^30 bytes (in base 2)

Since: 1 byte = 8 bits, 1 Tib = 2^40 bits = 2^37 bytes (in base 2).

Steps for Conversion

1. Convert Tebibits to bits: 1 Tib = 2^40 bits

2. Convert the daily rate to an hourly rate: Since there are 24 hours in a day, The hourly rate = $\frac{2^{40}}{24}$ bits per hour.

3. Convert bits to bytes: 1 byte = 8 bits, $\frac{2^{40}}{24 \times 8}$ bytes per hour.

4. Convert bytes to Gigabytes: In base 2, 1 GB = 2^30 bytes, In base 10, 1 GB = 10^9 bytes.

5. Calculations: Using the above data, let's go through the calculations.

Base 2 Conversion

1. Convert Tebibits to bits: 1 Tib = 2^40 bits

2. Convert to hourly rate: 2^40 bits per day ÷ 24 hours = $\frac{2^{40}}{24}$ bits per hour

3. Convert to bytes: $\frac{2^{40}}{24}$ bits per hour × $\frac{1}{8}$ bytes per bit = $\frac{2^{40}}{24 \times 8}$ bytes per hour = $\frac{2^{40}}{192}$ bytes per hour

4. Convert to Gigabytes in base 2: $\frac{2^{40}}{192 \times 2^{30}} = \frac{2^{10}}{192} = \frac{1024}{192} ≈ 5.33$ GiB per hour.

Base 10 Conversion

1. Base is the same until converting byte to GB: Convert to hourly rate: 2^40 bits per day ÷ 24 hours = $\frac{2^{40}}{24}$ bits per hour

2. Convert to bytes: $\frac{2^{40}}{24}$ bits per hour × $\frac{1}{8}$ bytes per bit = $\frac{2^{40}}{24 \times 8}$ bytes per hour = $\frac{2^{40}}{192}$ bytes per hour

3. Convert to Gigabytes in base 10: Using 1 GB = 10^9 bytes, $\frac{2^{40}}{192 \times 10^9} ≈ \frac{1.0995 \times 10^{12}}{192 \times 10^9} ≈ \frac{1.0995}{0.192} ≈ 5.73$ GB per hour.

Real-World Examples

Here are a few quantities and what they mean using the base 2 conversion (binary prefix):

1. 0.5 Tib/day: $0.5 \text{ Tib/day} \times \frac{5.33 \text{ GiB/hour}}{1 \text{ Tib/day}} = 2.665 \text{ GiB/hour}$.

2. 1 Tib/day: Roughly 5.33 GiB/hour as computed above.

3. 5 Tib/day: $5 \text{ Tib/day} \times \frac{5.33 \text{ GiB/hour}}{1 \text{ Tib/day}} = 26.65 \text{ GiB/hour}$.

4. 10 Tib/day: $10 \text{ Tib/day} \times \frac{5.33 \text{ GiB/hour}}{1 \text{ Tib/day}} = 53.3 \text{ GiB/hour}$.

Summary

• Base 2: 1 Tebibit/day ≈ 5.33 GiB/hour.
• Base 10: 1 Tebibit/day ≈ 5.73 GB/hour.

By considering these conversions, you can understand the data transfer rate better and contextualize it with real-world examples.