Gigabits per second to Mebibits per hour conversion

How to convert gigabits per second to mebibits per hour?

Certainly! Converting 1 Gigabit per second (Gbps) to Mebibits per hour (Mib/h) involves understanding the relationships between various units in both base 10 and base 2 systems.

Base 10 (Decimal) Conversion:

1. Convert Gigabits per second to Megabits per second (Mbps):

   • 1 Gbps = 1,000 Mbps

2. Find how many seconds are in an hour:

   • 1 hour = 3,600 seconds

3. Convert Megabits per second to Megabits per hour:

   • $1,000 \text{ Mbps}$ × $3,600 \text{ seconds/hour}$ = $3,600,000 \text{ Megabits/hour}$

4. Convert Megabits to Mebibits:

   • In base 10, 1 Megabit (Mb) = $10^6$ bits
   • In base 2, 1 Mebibit (Mib) = $2^{20}$ bits

So, 1 Megabit (Mb) in base 10 is $1,000,000$ bits and 1 Mebibit (Mib) is $1,048,576$ bits. This difference is crucial to convert properly:

• Convert Megabits to Mebibits: $\frac{3,600,000 \text{ Megabits}}{(1,048,576 / 1,000,000) \text{ Mebibits}}$
• Simplify the conversion factor: $1,048,576 / 1,000,000 = 1.048576$
• Therefore, $3,600,000 \text{ Megabits} ÷ 1.048576 = 3,434,314.58 \text{ Mebibits}$

So, 1 Gbps corresponds to approximately 3,434,314.58 Mib/h in Base 10.

Base 2 (Binary) Conversion:

1. Convert Gigabits per second to Gibibits per second (Gibps):

   • 1 Gbps = 1,000,000,000 bits per second
   • 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits
   • Therefore, $1 Gbps = \frac{1,000,000,000 bits}{\frac{1,073,741,824 bits}{2^{20}}}$ = $\approx 0.9313 Gibps$

2. Convert Gibibits per second to Mebibits per second (Mibps):

   • 1 Gibibit = 1,024 Mebibits (because $2^{30} / 2^{20} = 2^{10} = 1,024$)
   • So, $0.9313 Gibps \times 1,024 Mibps/Gibps \approx 953.67 Mibps$

3. Convert Mebibits per second to Mebibits per hour:

   • $953.67 \text{ Mibps} \times 3,600 \text{ seconds/hour} = 3,432,012 \text{ Mib/h}$

So, in base 2, 1 Gbps corresponds to approximately 3,432,012 Mib/h.

Real World Examples for Different Quantities of Gbps:

• 10 Gbps Internet Connection:

  • Base 10: 10 Gbps = 34,343,145.8 Mib/h
  • Base 2: 10 Gbps = 34,320,120 Mib/h

• Fiber Optic Lightpath for Data Centers (e.g., 100 Gbps):

  • Base 10: 100 Gbps = 343,431,458 Mib/h
  • Base 2: 100 Gbps = 343,201,200 Mib/h

• Broadband Cable e.g., DOCSIS 3.1 at 1.2 Gbps:

  • Base 10: 1.2 Gbps = 4,125,177.96 Mib/h
  • Base 2: 1.2 Gbps = 4,118,414.4 Mib/h

These conversions and real-world examples provide a comprehensive understanding of how different Gigabit per second rates translate into Mebibits per hour, depending on whether the base 10 or base 2 system is used.