Gibibytes per second to Terabits per day conversion

How to convert gibibytes per second to terabits per day?

Sure, let's walk through the conversion of Gibibytes per second (GiB/s) to Terabits per day (Tb/day) and cover both base 10 (decimal) and base 2 (binary) systems.

Base 2 (Binary) Conversion

1 Gibibyte (GiB) = 2^30 bytes (Binary) 1 byte = 8 bits

To find 1 GiB in bits: $1 \text{ GiB} = 2^{30} \text{ bytes}$ $1 \text{ byte} = 8 \text{ bits}$ $1 \text{ GiB} = 2^{30} \times 8 \text{ bits} = 2^{33} \text{ bits}$

1 second = 1 second (obviously) 1 day = 86400 seconds (24 hours * 60 minutes * 60 seconds)

So, 1 GiB/s in bits per second: $1 \text{ GiB/s} = 2^{33} \text{ bits/s}$

Now calculate per day: $2^{33} \text{ bits} \times 86400 \text{ s/day} = 2^{33} \times 86400 \text{ bits/day}$

Simplify this calculation using a calculator: $2^{33} \approx 8,589,934,592$ $8,589,934,592 \times 86400 = 742 \times 10^{12} \text{ bits/day}$

To convert bits to terabits (1 Tb = 10^{12} bits): $742 \times 10^{12} \text{ bits/day} = 742 \text{ Tb/day}$

Base 10 (Decimal) Conversion

1 Gibibyte (GiB) in base 10 is usually referred to as a Gigabyte (GB), where: 1 Gigabyte (GB) = 10^9 bytes (Decimal) 1 byte = 8 bits

So, 1 GB: $1 \text{ GB} = 10^9 \text{ bytes}$ $1 \text{ byte} = 8 \text{ bits}$ $1 \text{ GB} = 8 \times 10^9 \text{ bits}$

1 second = 1 second (obviously) 1 day = 86400 seconds (24 hours * 60 minutes * 60 seconds)

1 GB/s in bits per second: $1 \text{ GB/s} = 8 \times 10^9 \text{ bits/s}$

Now calculate per day: $8 \times 10^9 \text{ bits} \times 86400 \text{ s/day} = 691.2 \times 10^{12} \text{ bits/day}$

To convert to terabits: $691.2 \times 10^{12} \text{ bits/day} = 691.2 \text{ Tb/day}$

Summary:

• In base 2 (binary), 1 GiB/s ≈ 742 Tb/day.
• In base 10 (decimal), 1 GiB/s ≈ 691.2 Tb/day.

Real-World Examples of Data Transfer Rates:

1. Streaming Services: Netflix 4K UHD streaming: Approximately 25 Mbps. That's about $25 \times 60 \times 60 \times 24 / (8 \times 10^12) \approx 0.0027$ Gb/day.

2. Large Hadron Collider (LHC): The LHC produces about 30 Petabytes (30,000 Terabytes) of data per year.

   • Data per day: $30,000 \text{ TB/year} / 365 \approx 82.2 \text{ TB/day}$.

3. Cloud Data Center: High data transfer within a cloud data center might reach 1 Terabyte per second (TB/s), which translates to:

   • $1 \text{ TB/s} \times 86400 \text{ s/day} = 86400 \text{ TB/day}$.
   • Total in Terabits $86400 \text{ TB/day} \times 8 = 691,200 \text{ Tb/day}$.

These examples illustrate the scale of data transfer rates in a variety of contexts.