Tebibytes per hour to Gigabits per second conversion

How to convert tebibytes per hour to gigabits per second?

To convert 1 Tebibyte per hour to Gigabits per second (Gbps), we need to consider the following:

1. Understanding the units:

   • Tebibytes (TiB): A Tebibyte is a binary unit of data equal to $2^{40}$ bytes, or 1,099,511,627,776 bytes.
   • Hours to Seconds: There are 3600 seconds in an hour.
   • Bits and Bytes: 1 byte = 8 bits.
   • Base 10 versus Base 2:
     • Base 2 (Binary) Units: Tebibytes (TiB) directly relate to binary prefixes (e.g., 1 TiB = $2^{40}$ bytes).
     • Base 10 (Decimal) Units (Commonly termed as Terabytes, TB): 1 TB = $10^{12}$ bytes, but this is different from a Tebibyte.

2. Calculations for Base 2:

   • Step 1: Convert Tebibytes to bytes: $1 \text{ TiB} = 2^{40} \text{ bytes} = 1,099,511,627,776 \text{ bytes}$
   • Step 2: Convert bytes to bits: $1,099,511,627,776 \text{ bytes} \times 8 \text{ bits/byte} = 8,796,093,022,208 \text{ bits}$
   • Step 3: Convert hours to seconds: $1 \text{ hour} = 3600 \text{ seconds}$
   • Step 4: Calculate the rate in bits per second: $\frac{8,796,093,022,208 \text{ bits}}{3600 \text{ seconds}} = 2,443,359,172.836 \text{ bits per second}$
   • Step 5: Convert to Gigabits per second (1 Gbps = $10^9$ bits per second): $2,443,359,172.836 \text{ bits per second} \approx 2.443 \text{ Gbps}$

3. Calculations for Base 10:

   • Suppose we talk about "Terabyte" but still call it Tebibyte in a commercial aspect (TB instead of TiB):
   • Step 1: Convert 1 Terabyte to bytes: $1 \text{ TB} = 10^{12} \text{ bytes}$
   • Step 2: Convert bytes to bits: $10^{12} \text{ bytes} \times 8 \text{ bits/byte} = 8 \times 10^{12} \text{ bits} = 8,000,000,000,000 \text{ bits}$
   • Step 3: Convert hours to seconds: $1 \text{ hour} = 3600 \text{ seconds}$
   • Step 4: Calculate the rate in bits per second: $\frac{8,000,000,000,000 \text{ bits}}{3600 \text{ seconds}} = 2,222,222,222.222 \text{ bits per second}$
   • Step 5: Convert to Gigabits per second (1 Gbps = $10^9$ bits per second): $2,222,222,222.222 \text{ bits per second} = 2.222 \text{ Gbps}$

4. Real World Examples for Other Quantities:

   Example 1:

   • 5 Tebibytes per hour:
     • Using the same formula: $5 \text{ TiB/hr} \times 2.443 \text{ Gbps/TiB/hr} = 12.215 \text{ Gbps}$

   Example 2:

   • 10 Tebibytes per hour:
     • Using the similar conversion: $10 \text{ TiB/hr} \times 2.443 \text{ Gbps/TiB/hr} = 24.43 \text{ Gbps}$

   Example 3:

   • 20 Tebibytes per hour:
     • Conversion for base 2: $20 \text{ TiB/hr} \times 2.443 \text{ Gbps/TiB/hr} = 48.86 \text{ Gbps}$

In summary:

• Base 2 Conversion (Tebibytes): 1 TiB/hr ≈ 2.443 Gbps.
• Base 10 Conversion (Terabytes marketed as Tebibytes): 1 TB/hr ≈ 2.222 Gbps.