Bytes per second to Gigabytes per day conversion

How to convert bytes per second to gigabytes per day?

Sure, let's walk through the conversion of 1 Byte per second (Bps) to Gigabytes per day (GB/day). We'll start with the base 10 system (also known as decimal) and then move to the base 2 system (also known as binary).

Base 10 Conversion (Decimal)

In the decimal system:

• 1 Gigabyte (GB) = 1,000,000,000 Bytes (B)
• 1 day = 24 hours = 24 × 60 minutes = 24 × 60 × 60 seconds = 86,400 seconds

Given: 1 Byte per second (Bps)

To find: $\text{Gigabytes per day (GB/day)} = \frac{\text{Bytes per second} \times \text{seconds per day}}{1,000,000,000}$

Calculation: $\text{GB/day} = \frac{1 \text{ Bps} \times 86,400 \text{ seconds}}{1,000,000,000}$

$\text{GB/day} = \frac{86,400 \text{ Bytes}}{1,000,000,000}$

$\text{GB/day} = 0.0000864 \text{ GB/day}$

Thus, 1 Byte per second is 0.0000864 Gigabytes per day in the base 10 system.

Base 2 Conversion (Binary)

In the binary system:

• 1 Gigabyte (GiB) = 1,073,741,824 Bytes (2^30 Bytes)
• 1 day = 86,400 seconds (no change here)

Given: 1 Byte per second (Bps)

To find: $\text{Gibibytes per day (GiB/day)} = \frac{\text{Bytes per second} \times \text{seconds per day}}{1,073,741,824}$

Calculation: $\text{GiB/day} = \frac{1 \text{ Bps} \times 86,400 \text{ seconds}}{1,073,741,824}$

$\text{GiB/day} = \frac{86,400 \text{ Bytes}}{1,073,741,824}$

$\text{GiB/day} \approx 0.0000805 \text{ GiB/day}$

So, 1 Byte per second is approximately 0.0000805 GiB per day in the base 2 system.

Real-World Examples

Let’s explore some real-world data transfer rates to make this concept clearer.

Example 1: Common Broadband Speed

Assume an internet speed of 10 Megabytes per second (MBps).

• In base 10: $10 \text{ MBps} = 10,000,000 \text{ Bps}$ $\text{GB/day} = \frac{10,000,000 \text{ Bps} \times 86,400 \text{ sec}}{1,000,000,000}$ $\text{GB/day} = 864 \text{ GB/day}$

• In base 2: $10 \text{ MiBps} = 10 \times 1,048,576 \text{ Bps} = 10,485,760 \text{ Bps}$ $\text{GiB/day} = \frac{10,485,760 \text{ Bps} \times 86,400 \text{ sec}}{1,073,741,824}$ $\text{GiB/day} \approx 842 \text{ GiB/day}$

Example 2: USB 2.0 Data Transfer Speed

USB 2.0 can transfer data at a maximum of 480 Megabits per second (Mbps). Converting this to Bytes per second:

• 480 Mbps = 480,000,000 bits per second

• 1 Byte = 8 bits, so: $\text{Bps} = \frac{480,000,000}{8} = 60,000,000 \text{ Bps}$

• In base 10: $\text{GB/day} = \frac{60,000,000 \text{ Bps} \times 86,400 \text{ sec}}{1,000,000,000}$ $\text{GB/day} = 5,184 \text{ GB/day}$

• In base 2: $\text{GiB/day} = \frac{60,000,000 \text{ Bps} \times 86,400 \text{ sec}}{1,073,741,824}$ $\text{GiB/day} \approx 4,831 \text{ GiB/day}$

These examples demonstrate how different data transfer rates impact the amount of data transferred over a day, highlighting the practical significance of knowing how to convert between these units.