Gigabits per second to Bytes per hour conversion

How to convert gigabits per second to bytes per hour?

Sure! Let's break down the conversion of 1 Gigabit per second (Gbps) to Bytes per hour in both base 10 and base 2 systems.

Base 10 (Decimal)

In the base 10 system:

• 1 Gigabit (Gb) = 1,000,000,000 bits (b)
• 1 Byte (B) = 8 bits (b)

Steps:

1. Convert Gbps to bits per second: $1 \text{ Gbps} = 1,000,000,000 \text{ bits per second}.$
2. Convert bits per second to Bytes per second: $\text{Bytes per second} = \frac{\text{bits per second}}{8}$ $\text{Bytes per second} = \frac{1,000,000,000}{8} = 125,000,000 \text{ Bytes per second}$
3. Convert Bytes per second to Bytes per hour: Since there are 3600 seconds in an hour: $\text{Bytes per hour} = 125,000,000 \times 3600 = 450,000,000,000 \text{ Bytes per hour}$

Base 2 (Binary)

In the base 2 system:

• 1 Gibibit (Gib) = 2^30 bits (since 1 Gibibit = 1,073,741,824 bits)
• 1 Byte (B) = 8 bits (b)

But since it’s often more convenient to work with similar magnitude units, we’ll maintain Bit and Byte units then convert:

Steps:

1. Start with the equivalent bits in base 2 (binary): $1 \text{ Gbps} (base 2) = 1,000,000,000 \text{ bits per second}$
2. Convert bits per second to Bytes per second: $\text{Bytes per second} = \frac{\text{bits per second}}{8}$ $\text{Bytes per second} = \frac{1,000,000,000}{8} = 125,000,000 \text{ Bytes per second}$
3. Convert Bytes per second to Bytes per hour: Since there are 3600 seconds in an hour: $\text{Bytes per hour} = 125,000,000 \times 3600 = 450,000,000,000 \text{ Bytes per hour}$

It turns out that for simple conversion using Gigabits in base 10 versus bits per second in base 2 (both often approximated as 1,000,000,000 bits), the conversions happen to yield the same results if we're simply considering straightforward Bits and Bytes.

Real World Examples

Let's consider some different quantities of Gigabits per second in terms of usage cases in a typical or advanced scenario:

1. Home Internet Plan: 500 Mbps $0.5 \text{ Gbps}$ $\text{Bytes per second} = 125,000,000 \times 0.5 = 62,500,000 \text{ Bps}$ $\text{Bytes per hour} = 62,500,000 \times 3600 = 225,000,000,000 \text{ Bytes per hour}$

2. Corporate Data Network: 10 Gbps $\text{Bytes per second} = 10 \times 125,000,000 = 1,250,000,000 \text{ Bps}$ $\text{Bytes per hour} = 1,250,000,000 \times 3600 = 4,500,000,000,000 \text{ Bytes per hour}$

3. High-speed Data Center Link: 100 Gbps $\text{Bytes per second} = 100 \times 125,000,000 = 12,500,000,000 \text{ Bps}$ $\text{Bytes per hour} = 12,500,000,000 \times 3600 = 45,000,000,000,000 \text{ Bytes per hour}$

This provides a clear picture of data transfer capabilities of different Gbps speeds in terms of data that can be moved per hour.