Gigabits per second to Gibibits per day conversion

How to convert gigabits per second to gibibits per day?

Converting data transfer rates can be a bit challenging due to the differences between base 10 (decimal) and base 2 (binary) units. Let’s walk through the process of converting 1 Gigabit per second (Gbps) to Gibibits per day for both cases.

Base 10 (Decimal)

In decimal, 1 Gigabit (Gb) is equal to 1,000,000,000 bits.

To convert 1 Gbps to bits per second: $1 \text{ Gbps} = 1,000,000,000 \text{ bits per second}$

Now, to find out how many bits this is per day (since there are 86,400 seconds in a day): $1,000,000,000 \text{ bits/second} \times 86,400 \text{ seconds/day} = 86,400,000,000,000 \text{ bits/day}$

To find how many gigabits this is: $\frac{86,400,000,000,000 \text{ bits/day}}{1,000,000,000 \text{ bits/Gb}} = 86,400 \text{ Gb/day}$

Base 2 (Binary)

In binary, 1 Gibibit (Gib) is equal to $1024^3$ bits, which is: $1 \text{ Gib} = 1,073,741,824 \text{ bits}$

To convert 1 Gbps to bits per second in base 2: $1 \text{ Gbps} = 1,073,741,824 \text{ bits per second}$

Now, to find out how many bits this is per day: $1,073,741,824 \text{ bits/second} \times 86,400 \text{ seconds/day} = 92,233,720,368,640 \text{ bits/day}$

To find how many gibibits this is: $\frac{92,233,720,368,640 \text{ bits/day}}{1,073,741,824 \text{ bits/Gib}} \approx 85,899 \text{ Gib/day}$

Summary

• Base 10 (Decimal): 1 Gbps = 86,400 Gb/day
• Base 2 (Binary): 1 Gbps = 85,899 Gib/day

Real-world Examples with Other Quantities of Gbps

1. 10 Gbps Network Connection (Common in Data Centers)

   • Decimal: $10 \text{ Gbps} = 10 \times 86,400 \text{ Gb/day} = 864,000 \text{ Gb/day}$
   • Binary: $10 \text{ Gbps} = 10 \times 85,899 \text{ Gib/day} = 858,990 \text{ Gib/day}$

2. 1.5 Gbps Home Internet Connection

   • Decimal: $1.5 \text{ Gbps} = 1.5 \times 86,400 \text{ Gb/day} = 129,600 \text{ Gb/day}$
   • Binary: $1.5 \text{ Gbps} = 1.5 \times 85,899 \text{ Gib/day} \approx 128,848.5 \text{ Gib/day}$

3. 100 Gbps Large Enterprise Connection

   • Decimal: $100 \text{ Gbps} = 100 \times 86,400 \text{ Gb/day} = 8,640,000 \text{ Gb/day}$
   • Binary: $100 \text{ Gbps} = 100 \times 85,899 \text{ Gib/day} = 8,589,900 \text{ Gib/day}$

These examples should provide a comprehensive idea of how data transfer rates scale and what they represent in both decimal and binary forms.