bits per second to Gigabits per hour conversion

How to convert bits per second to gigabits per hour?

Sure! To convert bits per second to gigabits per hour, we need to understand what both units represent and perform the appropriate calculations.

1. Bits per second (bps): This is a unit of data transfer rate that specifies how many bits are transmitted in one second.

2. Gigabits (Gb): A gigabit is $10^9$ bits in base 10 and $2^{30}$ bits in base 2.

To convert bps to gigabits per hour, first convert seconds to hours and then bits to gigabits.

Base 10 (Decimal)

• Step 1: Convert seconds to hours. There are 3600 seconds in an hour.

  So, 1 bps = 1 bit/second.

  In one hour:

  $\text{Bits per hour} = 1 \text{ bps} \times 3600 \text{ seconds/hour} = 3600 \text{ bits/hour}$

• Step 2: Convert bits to gigabits (base 10). There are $10^9$ bits in a gigabit.

  $\text{Gigabits per hour} = \frac{3600 \text{ bits/hour}}{10^9 \text{ bits/Gigabit}} = 3.6 \times 10^{-6} \text{ Gigabits/hour}$

Base 2 (Binary)

• Step 1: Convert seconds to hours (same as above).

  $\text{Bits per hour} = 1 \text{ bps} \times 3600 \text{ seconds/hour} = 3600 \text{ bits/hour}$

• Step 2: Convert bits to gigabits (base 2). There are $2^{30}$ bits in a gigabit.

  $2^{30} = 1,073,741,824 \text{ bits}$

  $\text{Gigabits per hour} = \frac{3600 \text{ bits/hour}}{2^{30} \text{ bits/Gigabit}} = \frac{3600}{1,073,741,824} \text{ Gigabits/hour} \approx 3.35 \times 10^{-6} \text{ Gigabits/hour}$

So, the conversions are as follows:

• Base 10: $1 \text{ bits per second} = 3.6 \times 10^{-6} \text{ Gigabits per hour}$
• Base 2: $1 \text{ bits per second} = 3.35 \times 10^{-6} \text{ Gigabits per hour}$

Real-world examples for other quantities of bps:

1. 1 Kbps (1,000 bits per second) in base 10:

   • Base 10: $3.6 \times 10^{-3} \text{ Gigabits per hour}$
   • Base 2: $3.35 \times 10^{-3} \text{ Gigabits per hour}$

2. 1 Mbps (1,000,000 bits per second) in base 10:

   • Base 10: $3.6 \text{ Gigabits per hour}$
   • Base 2: $3.35 \text{ Gigabits per hour}$

3. 1 Gbps (1,000,000,000 bits per second) in base 10:

   • Base 10: $3,600 \text{ Gigabits per hour}$
   • Base 2: $3,355 \text{ Gigabits per hour}$

4. Internet speeds:

   • Typical broadband: 25 Mbps:
     • Base 10: $90 \text{ Gigabits per hour}$
     • Base 2: $83.75 \text{ Gigabits per hour}$

5. High-speed file transfer between servers:

   • 10 Gbps:
     • Base 10: $36,000 \text{ Gigabits per hour}$
     • Base 2: $33,550 \text{ Gigabits per hour}$

I hope this helps! Let me know if you need any more information.