Gigabits per day to Gibibits per hour conversion

How to convert gigabits per day to gibibits per hour?

To convert 1 gigabits per day (Gb/day) to gibibits per hour (Gibibits/hour), you need to understand the differences between the base 10 and base 2 systems.

Base 10 (Decimal System)

In the decimal system, a gigabit (Gb) is $10^9$ bits.

1. Convert gigabits per day to gigabits per hour:
   There are 24 hours in a day. $\frac{1 \text{ Gb/day}}{24 \text{ hours/day}} = 0.0416667 \text{ Gb/hour}$

2. Convert gigabits to gibibits (base 2):
   In the binary system, a gibibit (Gib) is $2^{30}$ bits. 1 Gb in base 10 is equal to $\frac{10^9}{2^{30}}$ ($10^{9}$ bits divided by $2^{30}$).

   Calculating: $1 \text{ Gb} = \frac{10^9}{2^{30}} \approx 0.9313 \text{ Gib}$

3. Convert gigabits per hour to gibibits per hour: $0.0416667 \text{ Gb/hour} \times 0.9313 \text{ Gib/Gb} \approx 0.0388 \text{ Gib/hour}$

So, in base 10: $1 \text{ Gb/day} \approx 0.0388 \text{ Gib/hour}$

Base 2 (Binary System)

In the binary system, we're dealing with gibibits (Gib).

1. Convert gigabits to gibibits:
   In this case, we're considering the gigabit as $2^{30}$ bits.

   Thus, 1 Gb/day is converted directly using base 2: $1 \text{ Gb} = 2^{30} \text{ bits}$ Daily conversion: $1 \text{ Gb/day} = 2^{30} \text{ bits/day}$

2. Convert this to gibibits per hour: $1 \text{ Gb/day} = \frac{2^{30}}{24 \times 2^{30}} \text{ Gib/hour}$ Since we are equating Gib in base 2: $1 \text{ Gib/day} = 2^{30}/2^{30}=1 \approx 0.0416667 \text{ Gib/hour}$

So, in base 2: $1 \text{ Gb/day} = 0.0416667 \text{ Gib/hour}$

Real-World Examples of Different Quantities

1. Streaming Media:

   • A compact disc (700 MB) is equivalent to approximately 5.6 Gb. Thus, if you were transferring one CD's worth of data per day, it would be approximately 5.6 Gb/day.

2. Office Networks:

   • A medium-sized office with average web usage might transfer around 100 Gb/day. In Gib/hour (base 10): $100 \text{ Gb/day} \approx 100 \times 0.0388 \approx 3.88 \text{ Gib/hour}$

3. Data Centers:

   • A data center might handle around 10,000 Gb/day. Converting to Gib/hour (base 10): $10000 \text{ Gb/day} \approx 10000 \times 0.0388 \approx 388 \text{ Gib/hour}$

Understanding these conversions helps in various contexts like network planning, bandwidth allocation, and understanding data transfer capabilities and limitations.