Gigabits per second to Mebibytes per second conversion

How to convert gigabits per second to mebibytes per second?

Sure, let's go through the conversion from Gigabits per second (Gbps) to Mebibytes per second (MiBps) step by step.

Base 10 (Decimal)

In base 10, the conversions are straightforward because they use powers of 10: 1 gigabit (Gb) = 1,000,000,000 bits 1 byte (B) = 8 bits 1 megabyte (MB) = 1,000,000 bytes

Steps:

1. Convert gigabits to bits: $1 \, \text{Gbps} = 1,000,000,000 \, \text{bits per second}$

2. Convert bits to bytes: $1,000,000,000 \, \text{bits per second} \div 8 = 125,000,000 \, \text{bytes per second}$

3. Convert bytes to megabytes: $125,000,000 \, \text{bytes per second} \div 1,000,000 = 125 \, \text{MBps}$

However, since we need Mebibytes in base 2, we must use powers of 2.

Base 2 (Binary)

1 gigabit (Gb) = 2^30 bits = 1,073,741,824 bits 1 byte (B) = 8 bits 1 mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes

Steps:

1. Convert gigabits to bits: $1 \, \text{Gbps} = 1 \times 2^{30} \, \text{bits per second} = 1,073,741,824 \, \text{bits per second}$

2. Convert bits to bytes: $1,073,741,824 \, \text{bits per second} \div 8 = 134,217,728 \, \text{bytes per second}$

3. Convert bytes to mebibytes: $134,217,728 \, \text{bytes per second} \div 1,048,576 = 128 \, \text{MiBps}$

Summary:

• Base 10 (Decimal): $1 \, \text{Gbps} = 125 \, \text{MBps}$
• Base 2 (Binary): $1 \, \text{Gbps} = 128 \, \text{MiBps}$

Real World Examples:

1. 10 Gbps Internet Service:

   • Base 10: $10 \, \text{Gbps}$ = 1250 MBps (megabytes per second)
   • Base 2: $10 \, \text{Gbps}$ = 1280 MiBps (mebibytes per second)

2. 1.5 Gbps Fiber Optic Connection:

   • Base 10: $1.5 \, \text{Gbps} = 187.5 \, \text{MBps}$
   • Base 2: $1.5 \, \text{Gbps} = 192 \, \text{MiBps}$

3. 5 Gbps USB 3.0:

   • Base 10: $5 \, \text{Gbps}$ = 625 MBps
   • Base 2: $5 \, \text{Gbps}$ = 640 MiBps

These conversions and examples help illustrate how to handle data transfer rates in different units.