bits per second to Bytes per day conversion

How to convert bits per second to bytes per day?

To convert data rates from bits per second (bps) to Bytes per day, first understand the relationship between bits and Bytes. There are 8 bits in a Byte. Additionally, you must account for the amount of time (in seconds) in a day.

There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, so: $\text{Seconds per day} = 24 \times 60 \times 60 = 86,400$

Assuming 1 bit per second (bps): $\text{Bits per day} = 1 \text{ bps} \times 86,400 \text{ seconds per day} = 86,400 \text{ bits per day}$

Since there are 8 bits in a Byte: $\text{Bytes per day} = \frac{86,400 \text{ bits per day}}{8 \text{ bits per Byte}} = 10,800 \text{ Bytes per day}$

Base 10 vs Base 2 Differences

In typical usage, conversions are done using base-10 (decimal), but in computing, sizes are often reported in base-2 (binary). Here’s how to handle both:

1. Base 10 (Decimal):

   • 1 Kilobyte (KB) = 1,000 Bytes
   • 1 Megabyte (MB) = 1,000,000 Bytes

2. Base 2 (Binary):

   • 1 Kibibyte (KiB) = 1,024 Bytes
   • 1 Mebibyte (MiB) = 1,048,576 Bytes

Using Base 10, the conversion process remains the same as above: $\text{10,800 Bytes per day} = 10.8 \text{ KB per day (10,800 / 1,000)}$

Using Base 2, the conversion slightly changes due to the different byte sizes: $\text{Bytes per day in Base 2 units} = 10,800 \text{ bytes}$ $\text{Bytes per day in KiB} = \frac{10,800 \text{ bytes}}{1,024} \approx 10.55 \text{ KiB per day}$

Real World Examples for Other Quantities of Bits per Second

Let's consider a few more common data rates:

1. 56 kbps (kilobits per second) – Traditional Dial-Up Modem Speed

$56,000 \text{ bps} \times 86,400 \text{ seconds per day} = 4,838,400,000 \text{ bits per day}$ $\text{Bytes per day} = \frac{4,838,400,000 \text{ bits}}{8} = 604,800,000 \text{ Bytes per day}$ $\text{KB per day (Base 10)} = \frac{604,800,000}{1,000} = 604,800 \text{ KB} \approx 604.8 \text{ MB}$ $\text{KiB per day (Base 2)} = \frac{604,800,000}{1,024} \approx 590,625 \text{ KiB} \approx 577 \text{ MiB}$

2. 1 Mbps (megabit per second) – Residential Internet Speed

$1,000,000 \text{ bps} \times 86,400 \text{ seconds per day} = 86,400,000,000 \text{ bits per day}$ $\text{Bytes per day} = \frac{86,400,000,000 \text{ bits}}{8} = 10,800,000,000 \text{ Bytes per day}$ $\text{GB per day (Base 10)} = \frac{10,800,000,000}{1,000,000,000} = 10.8 \text{ GB}$ $\text{GiB per day (Base 2)} = \frac{10,800,000,000}{1,073,741,824} \approx 10.06 \text{ GiB}$

3. 100 Mbps (megabit per second) – High-Speed Internet

$100,000,000 \text{ bps} \times 86,400 \text{ seconds per day} = 8,640,000,000,000 \text{ bits per day}$ $\text{Bytes per day} = \frac{8,640,000,000,000 \text{ bits}}{8} = 1,080,000,000,000 \text{ Bytes per day}$ $\text{GB per day (Base 10)} = \frac{1,080,000,000,000}{1,000,000,000} = 1,080 \text{ GB} \approx 1.08 \text{ TB}$ $\text{TiB per day (Base 2)} = \frac{1,080,000,000,000}{1,099,511,627,776} \approx 0.983 \text{ TiB}$

I hope this provides a clear explanation of how to convert bps to Bytes per day and illustrates various real-world data rates!