Bytes per second to Megabits per second conversion

How to convert bytes per second to megabits per second?

Certainly! The process of converting bytes per second (Bps) to megabits per second (Mbps) involves understanding the relationship between different units of digital information, specifically bits, bytes, kilobytes, and megabytes, and the numerical bases (base 10 and base 2) used in computing.

1. Base 10 Conversion:

   • 1 byte (B) = 8 bits (b)
   • In base 10, 1 megabit (Mb) = 1,000,000 bits (10^6 bits)

   To convert bytes per second to megabits per second in base 10: $\text{Mbps (Base 10)} = \frac{\text{Bps} \times 8}{1,000,000}$

   Applying the conversion formula for 1 Bps: $\text{Mbps (Base 10)} = \frac{1 \times 8}{1,000,000} = \frac{8}{1,000,000} = 0.000008 \text{ Mbps}$

2. Base 2 Conversion:

   • 1 byte (B) = 8 bits (b)
   • In base 2, 1 megabit (Mib) = 1,048,576 bits (2^20 bits)

   To convert bytes per second to megabits per second in base 2: $\text{Mibps (Base 2)} = \frac{\text{Bps} \times 8}{1,048,576}$

   Applying the conversion formula for 1 Bps: $\text{Mibps (Base 2)} = \frac{1 \times 8}{1,048,576} = \frac{8}{1,048,576} \approx 0.00000763 \text{ Mibps}$

So, for 1 byte per second:

• In base 10, it converts to 0.000008 Mbps.
• In base 2, it converts to approximately 0.00000763 Mibps.

Real-world Examples for Different Quantities of Bytes per Second

1. 56 Kbps Modem (circa 1990s):

   • 56 Kbps = 56,000 bits per second
   • Bytes per second = 56,000 / 8 = 7,000 Bps

2. Standard Residential Internet Connection (~100 Mbps):

   • 100 Mbps = 100,000,000 bits per second
   • Bytes per second = 100,000,000 / 8 = 12,500,000 Bps (12.5 MBps)

3. Gigabit Ethernet (~1 Gbps):

   • 1 Gbps = 1,000,000,000 bits per second
   • Bytes per second = 1,000,000,000 / 8 = 125,000,000 Bps (125 MBps)

4. USB 3.0 (~5 Gbps):

   • 5 Gbps = 5,000,000,000 bits per second
   • Bytes per second = 5,000,000,000 / 8 = 625,000,000 Bps (625 MBps)

Conversion of these to Mbps (Base 10) / Mibps (Base 2):

1. 7,000 Bps:

   • Base 10: $\frac{7000 \times 8}{1,000,000} = 0.056 \text{ Mbps}$
   • Base 2: $\frac{7000 \times 8}{1,048,576} \approx 0.0535 \text{ Mibps}$

2. 12,500,000 Bps:

   • Base 10: $\frac{12,500,000 \times 8}{1,000,000} = 100 \text{ Mbps}$
   • Base 2: $\frac{12,500,000 \times 8}{1,048,576} \approx 95.3674 \text{ Mibps}$

3. 125,000,000 Bps:

   • Base 10: $\frac{125,000,000 \times 8}{1,000,000} = 1,000 \text{ Mbps}$
   • Base 2: $\frac{125,000,000 \times 8}{1,048,576} \approx 953.674 \text{ Mibps}$

4. 625,000,000 Bps:

   • Base 10: $\frac{625,000,000 \times 8}{1,000,000} = 5,000 \text{ Mbps}$
   • Base 2: $\frac{625,000,000 \times 8}{1,048,576} \approx 4,768.372 \text{ Mibps}$

These examples demonstrate how data transfer rates in bytes per second translate to more familiar internet speeds in megabits per second using both base 10 and base 2 conversions.