bits per second to Gibibytes per day conversion

How to convert bits per second to gibibytes per day?

Sure, converting bits per second (bps) to Gibibytes per day involves a few steps. The steps will include unit conversions and understanding the differences between base 10 (decimal) and base 2 (binary). Let’s break it down.

Base 10 (Decimal) Conversion

1. Bits to Bytes:

   • There are 8 bits in a byte.
   • 1 bps = 1 bit per second. In terms of bytes per second, it will be $\frac{1}{8}$ bytes per second.

2. Bytes to Gigabytes:

   • There are 1000 bytes in a kilobyte (kB), 1000 kilobytes in a megabyte (MB), 1000 megabytes in a gigabyte (GB), and 1000 gigabytes in a terabyte (TB).
   • So, there are $1000 \times 1000 \times 1000 \times 1000 = 10^{12}$ bytes in a terabyte, and $10^{9}$ bytes in a gigabyte (GB).

3. Bytes per Second to Bytes per Day:

   • There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.
   • So, the number of seconds in a day is $60 \times 60 \times 24 = 86400$ seconds.

4. Combining Everything:

   • Bytes per second in a day $= \left( \frac{1}{8} \right) \times 86400$ bytes per day.
   • Converting Bytes to Gigabytes: $\frac{\left(\frac{1}{8} \times 86400\right)}{10^9}$

   Therefore: $\text{1 bps to GB per day} = \frac{86400}{8 \times 10^9} = \frac{86400}{8000000000} = 0.0000108 \text{ GB per day}$

Base 2 (Binary) Conversion

1. Bits to Bytes:

   • There are 8 bits in a byte.
   • 1 bit per second will be $\frac{1}{8}$ bytes per second.

2. Bytes to Gibibytes:

   • There are 1024 bytes in a kibibyte (KiB), 1024 kibibytes in a mebibyte (MiB), 1024 mebibytes in a gibibyte (GiB).
   • So, there are $1024 \times 1024 \times 1024$ bytes in a gibibyte (GiB), which is $2^{30} = 1073741824$ bytes.

3. Bytes per Second to Bytes per Day:

   • The number of seconds in a day is $60 \times 60 \times 24 = 86400$ seconds.

4. Combining Everything:

   • Bytes per second per day = $\left( \frac{1}{8} \right) \times 86400$ bytes.
   • Converting bytes to Gibibytes: $\frac{\left(\frac{1}{8} \times 86400\right)}{2^{30}}$

   Therefore: $\text{1 bps to GiB per day} = \frac{86400}{8 \times 1073741824} = \frac{86400}{8589934592} ≈ 0.000010051 \text{ GiB per day}$

Real-World Examples

1. Internet Speed:

   • Standard broadband speeds might be around 25 Mbps. To convert this to Gibibytes per day: $\text{25 Mbps} \to \text{GiB per day} = 25 \times 0.000010051 \approx 0.00025125 \text{ GiB per day} \approx 0.25 \text{ GiB per day}$

2. Data Transfer in a Company Network:

   • A gigabit Ethernet connection runs at 1 Gbps. $\text{1 Gbps} \to \text{GiB per day} = 1000 \times 0.000010051 \approx 0.010051 \text{ GiB per day} \approx 10.05 \text{ GiB per day}$

3. Streaming Services:

   • HD video streaming might consume around 5 Mbps per stream. $\text{5 Mbps} \to \text{GiB per day} = 5 \times 0.000010051 \approx 0.000050255 \text{ GiB per day} \approx 0.05 \text{ GiB per day}$

These conversions help illustrate how different data rates translate into daily consumptions and give context to various digital activities.