Gibibits per hour to Megabytes per second conversion

How to convert gibibits per hour to megabytes per second?

To convert Gibibits per hour (Gib/h) to Megabytes per second (MB/s), we need to understand the relationships between the different units and how they can be converted.

Understanding the Units:

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

1 Megabyte (MB) is often considered:

• In base 10 (decimal) as: 1 MB = 1,000,000 bytes
• In base 2 (binary) as: 1 MB = 2^20 bytes = 1,048,576 bytes

*Note: 1 byte = 8 bits, so 1 MB in base 10 is 8,000,000 bits, and 1 MB in base 2 is 8,388,608 bits.

Conversion Steps:

Step 1: Convert Gibibits to bits $1 \text{ Gibibit} = 2^{30} \text{ bits}$ $1 \text{ Gibibit per hour} = 1 \times 2^{30} \text{ bits per hour}$ $= 1,073,741,824 \text{ bits per hour}$

Step 2: Convert bits per hour to bits per second $1 \text{ hour} = 3600 \text{ seconds}$ $\text{bits per second} = \frac{\text{bits per hour}}{3600}$ $= \frac{1,073,741,824 \text{ bits}}{3600 \text{ seconds}}$ $= 298,262.73 \text{ bits per second} \text{ (approximately)}$

Step 3: Convert bits per second to Megabytes per second

Base 10 (Decimal):

$1 \text{ Megabyte} = 1,000,000 \text{ bytes} = 8,000,000 \text{ bits}$ $\text{MB/s in base 10} = \frac{\text{bits per second}}{8,000,000}$ $= \frac{298,262.73 \text{ bits per second}}{8,000,000}$ $= 0.037283 \text{ MB/s} \text{ (approximately)}$

Base 2 (Binary):

$1 \text{ Megabyte} = 2^{20} \text{ bytes} = 1,048,576 \text{ bytes} = 8,388,608 \text{ bits}$ $\text{MB/s in base 2} = \frac{\text{bits per second}}{8,388,608}$ $= \frac{298,262.73 \text{ bits per second}}{8,388,608}$ $= 0.03556 \text{ MB/s} \text{ (approximately)}$

Real-World Examples for Other Quantities of Gibibits per Hour:

Example 1: 10 Gibibits per Hour

• Convert to bits: $10 \text{ Gib} = 10 \times 1,073,741,824 = 10,737,418,240 \text{ bits per hour}$
• Bits per second: $10,737,418,240 \div 3600 = 2,982,627.33 \text{ bits per second}$
• In MB/s (Base 10): $\frac{2,982,627.33}{8,000,000} = 0.372828 \text{ MB/s}$
• In MB/s (Base 2): $\frac{2,982,627.33}{8,388,608} = 0.355615 \text{ MB/s}$

Example 2: 100 Gibibits per Hour

• Convert to bits: $100 \text{ Gib} = 100 \times 1,073,741,824 = 107,374,182,400 \text{ bits per hour}$
• Bits per second: $107,374,182,400 \div 3600 = 29,826,273.33 \text{ bits per second}$
• In MB/s (Base 10): $\frac{29,826,273.33}{8,000,000} = 3.728283 \text{ MB/s}$
• In MB/s (Base 2): $\frac{29,826,273.33}{8,388,608} = 3.556153 \text{ MB/s}$

These examples help illustrate the process of converting data transfer rates from Gibibits per hour to Megabytes per second in both base 10 and base 2.