Gigabits per second to Terabytes per hour conversion

How to convert gigabits per second to terabytes per hour?

To convert 1 Gigabit per second (Gbps) to Terabytes per hour (TB/hr), you first need to understand the relationship between these units in both base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal) System

1 byte (B) = 8 bits (b) 1 kilobyte (KB) = 1,000 bytes (B) 1 megabyte (MB) = 1,000 KB = 1,000,000 bytes 1 gigabyte (GB) = 1,000 MB = 1,000,000,000 bytes 1 terabyte (TB) = 1,000 GB = 1,000,000,000,000 bytes

Steps:

1. Convert Gigabits to Gigabytes: $1 \text{ Gbps} = \frac{1 \text{ Gigabit per second}}{8} = \frac{1 \text{ Gbps}}{8} = 0.125 \text{ GBps}$

2. Convert seconds to hours: $1 \text{ hour} = 3600 \text{ seconds}$

3. Convert GBps to GB/hr: $0.125 \text{ GBps} \times 3600 \text{ s/hr} = 450 \text{ GB/hr}$

4. Convert GB/hr to TB/hr: $450 \text{ GB/hr} \div 1000 = 0.45 \text{ TB/hr}$

Therefore, in the base 10 system: $1 \text{ Gbps} = 0.45 \text{ TB/hr} \text{ (base 10)}$

Base 2 (Binary) System

1 byte (B) = 8 bits (b) 1 kibibyte (KiB) = 1,024 bytes (B) 1 mebibyte (MiB) = 1,024 KiB = 1,048,576 bytes 1 gibibyte (GiB) = 1,024 MiB = 1,073,741,824 bytes 1 tebibyte (TiB) = 1,024 GiB = 1,099,511,627,776 bytes

Steps:

1. Convert Gigabits to Gibibytes: $1 \text{ Gbps} = \frac{1 \text{ Gigabit per second}}{8} = \frac{1 \text{ Gbps}}{8} = 0.125 \text{ GBps}$ Note: For simplicity, we can assume that the conceptual metric conversions apply similarly in binary, but remember that GiB to TiB involves base 2.

2. Convert seconds to hours: $1 \text{ hour} = 3600 \text{ seconds}$

3. Convert GBps to GB/hr: $0.125 \text{ GBps} \times 3600 \text{ s/hr} = 450 \text{ GB/hr}$

   Now, convert these 450 GB in binary terms:

   Since 1 GiB = 1,073,741,824 bytes, $450 \text{ GB} \times \frac{10^9 bytes}{2^{30} bytes} \approx 419.43 \text{ GiB}$

4. Convert GiB/hr to TiB/hr: $419.43 \text{ GiB/hr} \div 1024 \approx 0.4096 \text{ TiB/hr}$

Therefore, in the base 2 system: $1 \text{ Gbps} = 0.4096 \text{ TiB/hr} \text{ (base 2)}$

Real-World Examples:

1. 10 Gbps (Base 10): $10 \text{ Gbps} = 10 \times 0.45 = 4.5 \text{ TB/hr (base 10)}$

2. 100 Gbps (Base 10): $100 \text{ Gbps} = 100 \times 0.45 = 45 \text{ TB/hr (base 10)}$

3. 10 Gbps (Base 2): $10 \text{ Gbps} = 10 \times 0.4096 = 4.096 \text{ TiB/hr (base 2)}$

4. 100 Gbps (Base 2): $100 \text{ Gbps} = 100 \times 0.4096 = 40.96 \text{ TiB/hr (base 2)}$

By this, you can see how the conversion reflects depending on whether you use base 10 (decimal) or base 2 (binary) systems.