Bytes per second to Gigabits per hour conversion

How to convert bytes per second to gigabits per hour?

Sure! Let's break down the steps to convert from Bytes per second (Bps) to Gigabits per hour (Gbph), and we will cover both base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal) Calculation

First, let’s convert Bytes per second to Gigabits per hour using the base 10 system.

1. Convert Bytes to Bits: $1 \text{ Byte} = 8 \text{ bits}$ $1 \text{ Bps} = 1 \times 8 \text{ bits per second (bps)} = 8 \text{ bps}$

2. Convert Bits per second to Bits per hour: $1 \text{ hour} = 3600 \text{ seconds}$ $\text{Bits per hour} = 8 \text{ bps} \times 3600 \text{ seconds} = 28800 \text{ bits per hour}$

3. Convert Bits to Gigabits (base 10): In base 10, $1 \text{ Gigabit} = 10^9 \text{ bits}$. $\text{Gigabits per hour} = \frac{28800 \text{ bits}}{10^9 \text{ bits}} = 0.0000288 \text{ Gbph}$

So, 1 Byte per second is 0.0000288 Gigabits per hour in base 10.

Base 2 (Binary) Calculation

Now, let's do the same conversion but using the base 2 system.

1. Convert Bytes to Bits: $1 \text{ Byte} = 8 \text{ bits}$ $1 \text{ Bps} = 1 \times 8 \text{ bits per second (bps)} = 8 \text{ bps}$

2. Convert Bits per second to Bits per hour: $1 \text{ hour} = 3600 \text{ seconds}$ $\text{Bits per hour} = 8 \text{ bps} \times 3600 \text{ seconds} = 28800 \text{ bits per hour}$

3. Convert Bits to Gigabits (base 2): In base 2, $1 \text{ Gibibit} = 2^{30} \text{ bits} \approx 1.073741824 \times 10^9 \text{ bits}$. $\text{Gibibits per hour} = \frac{28800 \text{ bits}}{2^{30} \text{ bits}} = \frac{28800}{1,073,741,824} \approx 0.000026791 \text{ GiBph}$

So, 1 Byte per second is approximately 0.000026791 Gibibits per hour in base 2.

Real-world Examples:

• 10 Bytes per second:

  • In base 10: $10 \text{ Bps} = 10 \times 0.0000288 \text{ Gbph} = 0.000288 \text{ Gbph}$
  • In base 2: $10 \text{ Bps} = 10 \times 0.000026791 \text{ Gibph} = 0.00026791 \text{ GiBph}$

• 100 Bytes per second:

  • In base 10: $100 \text{ Bps} = 100 \times 0.0000288 \text{ Gbph} = 0.00288 \text{ Gbph}$
  • In base 2: $100 \text{ Bps} = 100 \times 0.000026791 \text{ Gibph} = 0.0026791 \text{ GiBph}$

• 1 Megabyte per second (1,000,000 Bytes per second in base 10 or $2^{20}$ Bytes per second in base 2):

  • In base 10: $1,000,000 \text{ Bps} = 1,000,000 \times 0.0000288 \text{ Gbph} = 28.8 \text{ Gbph}$
  • In base 2: $2^{20} \text{ Bps} \approx 1,048,576 \text{ Bps}$ $1,048,576 \text{ Bps} = 1,048,576 \times 0.000026791 \text{ GiBph} \approx 28.0448 \text{ GiBph}$

These examples show how different numbers of Bytes per second convert into Gigabits per hour using both base 10 and base 2 systems.