bits per second to Gibibits per hour conversion

How to convert bits per second to gibibits per hour?

To convert a data transfer rate from bits per second (bps) to Gibibits per hour (Gibibits/h), you need to understand the relationships between these units of measurement. Note that Gibibits (Gi) is based on a binary system (base 2), which is distinct from Gigabits (G) that are based on the decimal system (base 10).

Conversion Steps

Base 2 (Binary System):

1. 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits.
2. 1 hour = 3600 seconds.

Therefore, to convert bits per second to Gibibits per hour:

1. Multiply the rate in bits per second by the number of seconds in an hour to get bits per hour.
2. Convert the resulting number of bits to Gibibits.

Formula:

$\text{Gibibits per hour} = \left(\frac{\text{bps} \times 3600}{2^{30}}\right)$

Calculation:

1. $1 \text{ bits per second} \times 3600 \text{ seconds per hour} = 3600 \text{ bits per hour}$
2. $\frac{3600 \text{ bits per hour}}{1,073,741,824 \text{ bits per Gibibit}} = \frac{3600}{1,073,741,824} \approx 3.35 \times 10^{-6} \text{ Gibibits/hour}$

For Base 10 System (Decimal System):

1. 1 Gigabit (G) = 10^9 bits = 1,000,000,000 bits.
2. 1 hour = 3600 seconds.

To convert bits per second to Gigabits per hour in this system:

1. Multiply the rate in bits per second by the number of seconds in an hour to get bits per hour.
2. Convert the resulting number of bits to Gigabits.

Formula:

$\text{Gigabits per hour} = \left(\frac{\text{bps} \times 3600}{10^{9}}\right)$

Calculation:

1. $1 \text{ bits per second} \times 3600 \text{ seconds per hour} = 3600 \text{ bits per hour}$
2. $\frac{3600 \text{ bits per hour}}{1,000,000,000 \text{ bits per Gigabit}} = \frac{3600}{1,000,000,000} = 3.6 \times 10^{-6} \text{ Gigabits/hour}$

Summary:

• Base 2 (Binary): $1 \text{ bits per second} \approx 3.35 \times 10^{-6} \text{ Gibibits/hour}$
• Base 10 (Decimal): $1 \text{ bits per second} = 3.6 \times 10^{-6} \text{ Gigabits/hour}$

Real-World Examples:

1. Mobile Network Transfer Speed:

   • 4G LTE speed: Typically around 10 Mbps. $10 \text{ Megabits/second} = 10,000,000 \text{ bits/second}$ $10 \text{ Mbps} \approx 0.0335 \text{ Gibibits/hour (base 2)}$ $10 \text{ Mbps} = 0.036 \text{ Gigabits/hour (base 10)}$

2. Broadband Internet Speed:

   • 100 Mbps fiber connection: $100 \text{ Megabits/second} = 100,000,000 \text{ bits/second}$ $100 \text{ Mbps} \approx 0.335 \text{ Gibibits/hour (base 2)}$ $100 \text{ Mbps} = 0.36 \text{ Gigabits/hour (base 10)}$

3. Fast Ethernet:

   • 1 Gbps network: $1 \text{ Gigabit/second} = 1,000,000,000 \text{ bits/second}$ $1 \text{ Gbps} \approx 3.35 \text{ Gibibits/hour (base 2)}$ $1 \text{ Gbps} = 3.6 \text{ Gigabits/hour (base 10)}$

These examples illustrate how the basic unit conversion can be applied to understand network speeds and data transfer in real-world scenarios.