Gigabytes per second to Terabits per day conversion

How to convert gigabytes per second to terabits per day?

To convert data transfer rates between different units, it's important to understand the relationships between those units. Here's how you can convert 1 Gigabyte per second (GBps) to Terabits per day (Tb/day) using both base 10 (decimal) and base 2 (binary) conventions.

Base 10 (Decimal) Conversion

In base 10:

• 1 Gigabyte (GB) = 10^9 bytes
• 1 Terabit (Tb) = 10^12 bits
• 8 bits = 1 byte

Steps:

1. Convert Gigabytes to bits: $1 \text{ GB} = 1 \times 10^9 \text{ bytes} = 1 \times 10^9 \text{ bytes} \times 8 \text{ bits/byte} = 8 \times 10^9 \text{ bits}$

2. Convert seconds to days: $1 \text{ second} = \frac{1}{86400} \text{ days} \quad (\text{since } 86400 \text{ seconds = 1 day})$

3. Compute the data transferred in one day at 1 GBps: $\text{Data per day} = 8 \times 10^9 \text{ bits/second} \times 86400 \text{ seconds/day}$

4. Convert this to Terabits: $\text{Data per day in Tb} = \frac{8 \times 10^9 \text{ bits/second} \times 86400 \text{ seconds/day}}{10^{12} \text{ bits/Tb}}$

5. Perform the calculation: $= \frac{8 \times 10^9 \times 86400}{10^{12}} = \frac{691200000000000}{1000000000000} = 691.2 \text{ Terabits per day}$

Base 2 (Binary) Conversion

In base 2:

• 1 Gibibyte (GiB) = 2^{30} bytes
• 1 Tebibit (Tib) = 2^{40} bits
• 8 bits = 1 byte

Steps:

1. Convert Gibibytes to bits: $1 \text{ GiB} = 2^{30} \text{ bytes} = 2^{30} \text{ bytes} \times 8 \text{ bits/byte} = 2^{33} \text{ bits}$

2. Compute the data transferred in one day at 1 GiBps: $\text{Data per day} = 2^{33} \text{ bits/second} \times 86400 \text{ seconds/day}$

3. Convert this to Tebibits: $\text{Data per day in Tib} = \frac{2^{33} \text{ bits/second} \times 86400 \text{ seconds/day}}{2^{40} \text{ bits/Tib}}$

4. Simplify the equation: $= \frac{2^{33} \times 86400}{2^{40}} = \frac{86400}{2^{7}} = \frac{86400}{128} = 675 \text{ Tebibits per day}$

Summary

• In base 10: 1 GBps = 691.2 Terabits per day (Tb/day)
• In base 2: 1 GiBps = 675 Tebibits per day (Tib/day)

Real-World Examples for Other Quantities of Gigabytes per Second

1. 10 GBps: This rate is closer to what very high-end enterprise-level networks or scientific data transfer systems might achieve. $\text{Base 10: } 10 \text{ GBps} = 6912 \text{ Tb/day}$ $\text{Base 2: } 10 \text{ GiBps} = 6750 \text{ Tib/day}$

2. 1.25 GBps: This is equivalent to a 10 Gbps Ethernet link (10 Gbps $\approx$ 1.25 GBps). $\text{Base 10: } 1.25 \text{ GBps} = 863.25 \text{ Tb/day}$ $\text{Base 2: } 1.25 \text{ GiBps} = 843.75 \text{ Tib/day}$

3. 0.5 GBps: This might be typical for a high-speed consumer fiber-optic internet connection. $\text{Base 10: } 0.5 \text{ GBps} = 345.6 \text{ Tb/day}$ $\text{Base 2: } 0.5 \text{ GiBps} = 337.5 \text{ Tib/day}$

These examples demonstrate the immense amount of data that can be transferred with high-speed internet and network connections, which are crucial for modern data-intensive applications.