Gigabits per second to Megabytes per hour conversion

How to convert gigabits per second to megabytes per hour?

Sure, let's break down how to convert 1 Gigabit per second (Gbps) to Megabytes per hour (MB/hr). Note that data units have two different bases: base 10 (decimal) and base 2 (binary). They use different multipliers, so the answers will be different.

Base 10 (Decimal)

1 Gbps = 1 gigabit per second = 1,000,000,000 bits per second (because "giga" in base 10 is $10^9$).

1 byte = 8 bits.

So, 1 Gbps = $\frac{1,000,000,000 \text{ bits}}{1 \text{ second}} \times \frac{1 \text{ byte}}{8 \text{ bits}}$ = $125,000,000 \text{ bytes per second}$.

To convert seconds to hours, we note there are 3,600 seconds in an hour.

So, $125,000,000 \text{ bytes per second} \times 3,600 \text{ seconds per hour} = 450,000,000,000 \text{ bytes per hour}$

Convert bytes to megabytes: 1 MB (in base 10) = 1,000,000 bytes.

Thus, $450,000,000,000 \text{ bytes per hour} \div 1,000,000 = 450,000 \text{ MB per hour (base 10)}$

Base 2 (Binary)

1 Gbps = 1 gigabit per second = 2^30 bits per second (because "giga" in base 2 is $2^{30}$).

1 byte = 8 bits.

So, 1 Gbps = $\frac{2^{30} \text{ bits}}{1 \text{ second}} \times \frac{1 \text{ byte}}{8 \text{ bits}}$ = $2^{27} \text{ bytes per second}$ = $134,217,728 \text{ bytes per second}$.

To convert seconds to hours: $134,217,728 \text{ bytes per second} \times 3,600 \text{ seconds per hour} = 483,183,820,800 \text{ bytes per hour}$

Convert bytes to megabytes: 1 MB (in base 2) = 2^20 bytes = 1,048,576 bytes.

Thus, $483,183,820,800 \text{ bytes per hour} \div 1,048,576 = 460,800 \text{ MB per hour (base 2)}$

Summary

• 1 Gbps (base 10) to MB/hr: $450,000$ MB/hr
• 1 Gbps (base 2) to MB/hr: $460,800$ MB/hr

Real World Examples of Data Transfer Rates

1. 5 Gbps: Common speed for modern USB 3.0 interfaces.

   • Base 10: $2,250,000$ MB/hr
   • Base 2: $2,304,000$ MB/hr

2. 10 Gbps: Typical for high-speed Ethernet.

   • Base 10: $4,500,000$ MB/hr
   • Base 2: $4,608,000$ MB/hr

3. 100 Gbps: Often used in data centers and high-capacity backbone networks.

   • Base 10: $45,000,000$ MB/hr
   • Base 2: $46,080,000$ MB/hr

These quantities help illustrate the large amounts of data transfer that can occur in network systems and modern data storage solutions.