Bytes per second to Gibibits per second conversion

How to convert bytes per second to gibibits per second?

To convert from bytes per second (Bps) to gibibits per second (Gibps), you need to understand the following points:

1. Bytes and Bits:

   • 1 byte = 8 bits

2. Gigabit and Gibibit:

   • Gigabit (Gb) uses the base 10 system.
     • 1 gigabit (Gb) = 10^9 bits = 1,000,000,000 bits
   • Gibibit (Gib) uses the base 2 system.
     • 1 gibibit (Gib) = 2^30 bits = 1,073,741,824 bits

Conversion from Bytes per second to Gibibits per second

Base 10 (Gigabits per second, Gbps)

1. Multiply the number of bytes per second by 8 to get bits per second:
   • $1 \text{ Bps} \times 8 = 8 \text{ bps}$
2. Divide by 10^9 to convert to gigabits per second:
   • $\frac{8 \text{ bps}}{1,000,000,000} = 8 \times 10^{-9} \text{ Gbps}$

So, 1 Bps = 8 x 10^-9 Gbps.

Base 2 (Gibibits per second, Gibps)

1. Multiply the number of bytes per second by 8 to get bits per second:
   • $1 \text{ Bps} \times 8 = 8 \text{ bps}$
2. Divide by 2^30 to convert to gibibits per second:
   • $\frac{8 \text{ bps}}{1,073,741,824} \approx 7.45 \times 10^{-9} \text{ Gibps}$

So, 1 Bps ≈ 7.45 x 10^-9 Gibps.

Real-World Examples

1. Internet Speed

• 5 Megabytes per second (MBps):
  • In Base 10 (Gbps):
    • $5 \times 8 = 40 \text{ Mbps}$
    • $\frac{40 \text{ Mbps}}{1,000} = 0.04 \text{ Gbps}$
  • In Base 2 (Gibps):
    • $5 \text{ MBps} = 5 \times 1,048,576 \text{ bytes} = 5,242,880 \text{ bytes}$
    • $5,242,880 \times 8 \text{ bits} = 41,943,040 \text{ bits}$
    • $\frac{41,943,040}{1,073,741,824} \approx 0.039 \text{ Gibps}$

2. File Download Speed

• 50 Kilobytes per second (KBps):
  • In Base 10 (Gbps):
    • $50 \times 1,000 \text{ bytes} = 50,000 \text{ bytes}$
    • $50,000 \times 8 \text{ bits} = 400,000 \text{ bits}$
    • $\frac{400,000}{1,000,000,000} = 4 \times 10^{-4} \text{ Gbps}$
  • In Base 2 (Gibps):
    • $50 \times 1,024 = 51,200 \text{ bytes}$
    • $51,200 \times 8 = 409,600 \text{ bits}$
    • $\frac{409,600 \text{ bits}}{1,073,741,824} \approx 3.81 \times 10^{-4} \text{ Gibps}$

3. Video Streaming (High Definition)

• 10 Megabytes per second (MBps):
  • In Base 10 (Gbps):
    • $10 \times 8 = 80 \text{ Mbps}$
    • $\frac{80 \text{ Mbps}}{1,000} = 0.08 \text{ Gbps}$
  • In Base 2 (Gibps):
    • $10 \times 1,048,576 = 10,485,760 \text{ bytes}$
    • $10,485,760 \times 8 = 83,886,080 \text{ bits}$
    • $\frac{83,886,080 \text{ bits}}{1,073,741,824} \approx 0.078 \text{ Gibps}$

These examples demonstrate how to convert and get a sense of scale for data transfer rates in different units.