Gibibits per second to Gigabits per day conversion

How to convert gibibits per second to gigabits per day?

Sure, let's start with the conversion of 1 Gibibit per second (Gib/s) to Gigabits per day (Gb/day). The conversion process differs depending on whether we use base-2 or base-10.

Base-2 (Binary System)

1 Gibibit (Gib) is equal to $2^{30}$ bits. In terms of bits: $1 \text{ Gibibit} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$

Since we have 1 Gibibit per second: $1 \text{ Gib/s} = 1,073,741,824 \text{ bits per second}$

To find the total bits per day: $1 \text{ day} = 24 \text{ hours} \times 60 \text{ minutes per hour} \times 60 \text{ seconds per minute} = 86,400 \text{ seconds}$

So, multiplying our data rate by the number of seconds in a day: $1,073,741,824 \text{ bits per second} \times 86,400 \text{ seconds per day} = 92,233,720,368,640 \text{ bits per day}$

To convert bits to Gigabits (using base-2 definition): $1 \text{ Gigabit} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$

Therefore: $92,233,720,368,640 \text{ bits per day} \div 1,073,741,824 \text{ bits per Gigabit} = 85,184 \text{ Gb/day}$

Base-10 (Decimal System)

1 Gibibit (Gib) is still $2^{30}$ bits: $1 \text{ Gibibit} = 1,073,741,824 \text{ bits}$

But, a Gigabit in base-10 is: $1 \text{ Gigabit} = 10^9 \text{ bits} = 1,000,000,000 \text{ bits}$

The process for determining bits per day stays the same: $1,073,741,824 \text{ bits per second} \times 86,400 \text{ seconds per day} = 92,233,720,368,640 \text{ bits per day}$

To convert bits to Gigabits (base-10): $92,233,720,368,640 \text{ bits per day} \div 1,000,000,000 \text{ bits per Gigabit} = 92,233.72036864 \text{ Gb/day}$

Real World Examples for Other Quantities of Gibibits per Second

0.5 Gibibits per second

• Base-2: $0.5 \text{ Gib/s} = 0.5 \times 1,073,741,824 \text{ bits per second}$ $0.5 \times 86,400 \text{ seconds} = 46,116,860,184,320 \text{ bits per day}$ $\frac{46,116,860,184,320 \text{ bits per day}}{1,073,741,824 \text{ bits per Gigabit}} = 42,592 \text{ Gb/day}$

• Base-10: $\frac{46,116,860,184,320 \text{ bits per day}}{1,000,000,000 \text{ bits per Gigabit}} = 46,116.86018432 \text{ Gb/day}$

2 Gibibits per second

• Base-2: $2 \text{ Gib/s} = 2 \times 1,073,741,824 \text{ bits per second}$ $2 \times 86,400 \text{ seconds} = 184,467,440,737,280 \text{ bits per day}$ $\frac{184,467,440,737,280 \text{ bits per day}}{1,073,741,824 \text{ bits per Gigabit}} = 170,368 \text{ Gb/day}$

• Base-10: $\frac{184,467,440,737,280 \text{ bits per day}}{1,000,000,000 \text{ bits per Gigabit}} = 184,467.44073728 \text{ Gb/day}$

These examples illustrate how data transfer rates, expressed in Gibibits per second, can be converted to Gigabits per day, demonstrating the difference between the base-2 and base-10 definitions.