Megabytes per second to Gibibits per second conversion

How to convert megabytes per second to gibibits per second?

To convert Megabytes per second (MB/s) to Gibibits per second (Gib/s), you need to understand the differences in measurement units based on base 10 and base 2 systems.

Base 10 (Decimal) System

In base 10:

• 1 Megabyte (MB) = 1,000,000 bytes
• 1 byte = 8 bits
• Therefore, 1 MB = 8,000,000 bits

Base 2 (Binary) System

In base 2:

• 1 Mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes
• 1 byte = 8 bits
• Therefore, 1 MiB = 8,388,608 bits

Converting to Gibibits per Second (Gib/s)

In base 2:

• 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits

Conversion Calculations

Base 10:

1. First, convert Megabytes to bits: $1 \text{ MB} = 1,000,000 \text{ bytes} \times 8 \text{ bits/byte} = 8,000,000 \text{ bits}$
2. Then, convert bits to Gibibits: $1 \text{ Gib} = 1,073,741,824 \text{ bits}$ $\text{Gib/s} = \frac{8,000,000 \text{ bits}}{1,073,741,824 \text{ bits}} \approx 0.00745 \text{ Gib/s} \approx 7.45 \text{ Mbps}$

Base 2:

1. First, convert Mebibytes to bits: $1 \text{ MiB} = 1,048,576 \text{ bytes} \times 8 \text{ bits/byte} = 8,388,608 \text{ bits}$
2. Then, convert bits to Gibibits: $1 \text{ Gib} = 1,073,741,824 \text{ bits}$ $\text{Gib/s} = \frac{8,388,608 \text{ bits}}{1,073,741,824 \text{ bits}} \approx 0.0078125 \text{ Gib/s} \approx 7.8125 \text{ Mbps}$

Real World Examples for Other Quantities of MB/s

1. 10 MB/s:

   • Base 10: $\text{Gib/s} = \frac{10 \times 8,000,000 \text{ bits}}{1,073,741,824} \approx 0.0745 \text{ Gib/s} \approx 74.5 \text{ Mbps}$
   • Base 2: $\text{Gib/s} = \frac{10 \times 8,388,608 \text{ bits}}{1,073,741,824} \approx 0.078125 \text{ Gib/s} \approx 78.125 \text{ Mbps}$

2. 100 MB/s:

   • Base 10: $\text{Gib/s} = \frac{100 \times 8,000,000 \text{ bits}}{1,073,741,824} \approx 0.745 \text{ Gib/s} \approx 745 \text{ Mbps}$
   • Base 2: $\text{Gib/s} = \frac{100 \times 8,388,608 \text{ bits}}{1,073,741,824} \approx 0.78125 \text{ Gib/s} \approx 781.25 \text{ Mbps}$

3. 1,000 MB/s (1 GB/s):

   • Base 10: $\text{Gib/s} = \frac{1,000 \times 8,000,000 \text{ bits}}{1,073,741,824} \approx 7.45 \text{ Gib/s}$
   • Base 2: $\text{Gib/s} = \frac{1,000 \times 8,388,608 \text{ bits}}{1,073,741,824} \approx 7.8125 \text{ Gib/s}$

Real World Contexts

These conversions help when working with different storage and transmission standards such as hard drives, SSDs, network bandwidth, and internet service speeds. For example:

• A 4K video stream requires roughly 25 MB/s, which is:
  • Approximately 0.18625 Gib/s using base 10 conversion,
  • Approximately 0.1953125 Gib/s using base 2 conversion.

This can help you understand the data requirements and ensure compatible hardware and services.

Keep in mind these conversions primarily assist in accurately representing capacities and speeds across different systems and ensuring that technical specifications in different contexts are met correctly.