Gibibits per second to Megabits per second conversion

How to convert gibibits per second to megabits per second?

To convert from Gibibits per second (Gibit/s) to Megabits per second (Mbit/s), we need to understand the difference between the binary (base 2) and decimal (base 10) prefixes:

Base 2 Conversion

1 Gibibit (Gibit) is equal to $2^{30}$ bits, and 1 Megabit (Mbit) is equal to $2^{20}$ bits. Therefore, converting 1 Gibibit per second to Megabits per second in base 2:

$1 \text{ Gibit/s} = \frac{2^{30} \text{ bits}}{2^{20} \text{ bits/Mbit}} = 2^{10} \text{ Mbit/s} = 1024 \text{ Mbit/s}$

Base 10 Conversion

1 Gibibit (Gibit) is traditionally calculated in base 2 for binary data transfer rates, but for comparison, if using the more common base 10:

1 Gibibit = $2^{30}$ bits 1 Mbit = $10^6$ bits

$1 \text{ Gibit/s} = \frac{2^{30} \text{ bits}}{10^6 \text{ bits/Mbit}} = \frac{1073741824 \text{ bits}}{1000000 \text{ bits/Mbit}} = 1073.741824 \text{ Mbit/s}$

Real-world Examples

1. Network Speeds

   • A 10 Gibibit per second (Gibit/s) Ethernet connection:
     • In base 2: $10 \text{ Gibit/s} = 10 \times 1024 = 10240 \text{ Mbit/s}$
     • In base 10: $10 \text{ Gibit/s} = 10 \times 1073.741824 = 10737.41824 \text{ Mbit/s}$

2. Data Center Interconnects

   • A 40 Gibibit per second (Gibit/s) InfiniBand link:
     • In base 2: $40 \text{ Gibit/s} = 40 \times 1024 = 40960 \text{ Mbit/s}$
     • In base 10: $40 \text{ Gibit/s} = 40 \times 1073.741824 = 42949.67296 \text{ Mbit/s}$

3. High-Speed Storage Interfaces

   • NVMe SSDs with 4 Gibibit per second (Gibit/s) data transfer rate:
     • In base 2: $4 \text{ Gibit/s} = 4 \times 1024 = 4096 \text{ Mbit/s}$
     • In base 10: $4 \text{ Gibit/s} = 4 \times 1073.741824 = 4294.967296 \text{ Mbit/s}$

These examples illustrate how conversions are critical in different contexts, particularly in fields requiring precise data rate measurements.