bits per second to Gigabytes per second conversion

How to convert bits per second to gigabytes per second?

To convert bits per second (bps) to gigabytes per second (GBps), you need to understand the relationship between bits, bytes, and gigabytes. First, let's go through the basics:

1 byte = 8 bits

1 gigabyte (base 10) = 10^9 bytes 1 gigabyte (base 2) = 2^30 bytes

Conversion Steps:

Base 10 (decimal) Conversion:

1. Convert bits to bytes: Since 1 byte = 8 bits, you divide the number of bits by 8.

2. Convert bytes to gigabytes: Since 1 gigabyte (base 10) = 10^9 bytes, you divide the number of bytes by 10^9.

Given: 1 bps

Step 1: Convert bits to bytes: $\frac{1 \text{ bit}}{8} = 0.125 \text{ bytes/second}$

Step 2: Convert bytes to gigabytes: $\frac{0.125 \text{ bytes/second}}{10^9} = 1.25 \times 10^{-10} \text{ GBps}$

So, 1 bps = $1.25 \times 10^{-10}$ gigabytes per second (base 10).

Base 2 (binary) Conversion:

1. Convert bits to bytes: Again, 1 byte = 8 bits, so you divide by 8.

2. Convert bytes to gigabytes: Since 1 gigabyte (base 2) = 2^30 bytes, you divide the number of bytes by 2^30.

Given: 1 bps

Step 1: Convert bits to bytes: $\frac{1 \text{ bit}}{8} = 0.125 \text{ bytes/second}$

Step 2: Convert bytes to gigabytes: $\frac{0.125 \text{ bytes/second}}{2^{30}} = \frac{0.125}{1,073,741,824} \approx 1.164 \times 10^{-10} \text{ GBps}$

So, 1 bps = $1.164 \times 10^{-10}$ gigabytes per second (base 2).

Real-World Examples for Other Quantities:

1 kbps (kilobits per second):

• Base 10: $1.25 \times 10^{-7}$ GBps
• Base 2: $1.164 \times 10^{-7}$ GBps

1 Mbps (megabits per second):

• Base 10: $1.25 \times 10^{-4}$ GBps
• Base 2: $1.164 \times 10^{-4}$ GBps

1 Gbps (gigabits per second):

• Base 10: $1.25 \times 10^{-1}$ GBps
• Base 2: $1.164 \times 10^{-1}$ GBps

1 Tbps (terabits per second):

• Base 10: $1.25 \times 10^{2}$ GBps
• Base 2: $1.164 \times 10^{2}$ GBps

Real-World Use Cases:

1 kbps:

• Slow data connections, such as those used in some IoT devices or old dial-up modems.

1 Mbps:

• Standard internet plans for basic web browsing and low-quality video streaming.

1 Gbps:

• High-speed internet plans for households with multiple devices, providing fast downloads, 4K streaming, and online gaming.

1 Tbps:

• Ultra-high-speed connections for data centers, large enterprises, and scenarios requiring massive data transfer, such as for scientific simulations or city-wide fiber-optic networks.

I hope this clears up the conversions and gives you a sense of scale for different data transfer rates!