Gigabits per second to Kibibytes per day conversion

How to convert gigabits per second to kibibytes per day?

To convert 1 Gigabit per second (Gbps) to Kibibytes per day (KiB/day), we'll need to follow a series of steps, involving conversions within different units of data measurement and time intervals. We'll do this conversion for both base 10 (decimal) and base 2 (binary).

Base 10 (Decimal)

1. Convert Gigabits to bits:

   • 1 Gigabit (Gb) = 1,000,000,000 bits (b)

2. Convert bits to Kibibits:

   • 1 Kibibit (Kib) = 1,024 bits (base 2), so: $1,000,000,000 \, \text{bits} \div 1,024 \, \text{bits/Kib} = 976,562.5 \, \text{Kib}$

3. Convert Kibibits to Kibibytes:

   • 1 Kibibyte (KiB) = 8 Kibibits (Kib), so: $976,562.5 \, \text{Kib} \div 8 \, \text{Kib/KiB} = 122,070.3125 \, \text{KiB}$

4. Convert seconds to a day:

   • 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds = 86,400 seconds

5. Combine the rates:

   • Data rate × Time duration: $122,070.3125 \, \text{KiB/s} \times 86,400 \, \text{s/day} = 10,543,875,000 \, \text{KiB/day}$

Base 2 (Binary)

1. Convert Gigabits to Gibibits:

   • 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits
   • 1 Gigabit (Gb) = 1,000,000,000 bits
   • Conversion factor between Gb and Gib: $1 \text{Gb} = \frac{1,000,000,000}{1,073,741,824} \approx 0.9313 \text{Gib}$

2. Convert Gibibits to Kibibits:

   • 1 Gibibit (Gib) = 2^20 Kibibits (Kib)
   • $0.9313 \, \text{Gib} \times 2^20 \, \text{Kib/Gib} = 976,563 \, \text{Kib}$

3. Convert Kibibits to Kibibytes:

   • 1 Kibibyte (KiB) = 8 Kibibits (Kib), so: $976,563 \, \text{Kib} \div 8 \, \text{Kib/KiB} = 122,070.375 \, \text{KiB}$

4. Combine the rates:

   • Data rate × Time duration: $122,070.375 \, \text{KiB/s} \times 86,400 \, \text{s/day} \approx 10,543,876,000 \, \text{KiB/day}$

Real-World Examples

1. 10 Gbps (Google Fiber's internet service):

   • Decimal: $10 \, \text{Gbps} \times 10,543,875,000 \, \text{KiB/day/Gbps} = 105,438,750,000 \, \text{KiB/day}$
   • Binary: $10 \, \text{Gbps} \times 10,543,876,000 \, \text{KiB/day/Gbps} = 105,438,760,000 \, \text{KiB/day}$

2. 1.5 Gbps (A high-speed home internet plan):

   • Decimal: $1.5 \, \text{Gbps} \times 10,543,875,000 \, \text{KiB/day/Gbps} = 15,815,812,500 \, \text{KiB/day}$
   • Binary: $1.5 \, \text{Gbps} \times 10,543,876,000 \, \text{KiB/day/Gbps} \approx 15,815,814,000 \, \text{KiB/day}$

3. 30 Gbps (A backbone connection of a data center):

   • Decimal: $30 \, \text{Gbps} \times 10,543,875,000 \, \text{KiB/day/Gbps} = 316,316,250,000 \, \text{KiB/day}$
   • Binary: $30 \, \text{Gbps} \times 10,543,876,000 \, \text{KiB/day/Gbps} = 316,316,280,000 \, \text{KiB/day}$

In both base 10 and base 2 conversions, the difference is relatively small but may be significant in certain technical scenarios, particularly in data-intensive environments like data centers, ISPs, or high-traffic websites.