Gigabits per day to Tebibytes per second conversion

How to convert gigabits per day to tebibytes per second?

To convert from gigabits per day to tebibytes per second, we need to break down the conversion into two main parts: converting time units (from days to seconds) and converting data units (from gigabits to tebibytes). Let's dive into this step-by-step, including both the base-10 (decimal) and base-2 (binary) conversions.

Base-10 (Decimal) Conversion

1. Understand the Base Units:

• 1 gigabit = 10^9 bits
• 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds = 86,400 seconds

2. Convert Gigabits per Day to Bits per Second:

1 gigabit/day = (10^9 bits/day) / (86,400 seconds/day)

Calculation: $\frac{10^9 \text{ bits}}{86,400 \text{ seconds}} \approx 11,574.07 \text{ bits/second}$

3. Convert Bits per Second to Tebibytes per Second:

1 tebibyte (TiB) = 2^40 bits $11,574.07 \text{ bits/second} \approx \frac{11,574.07}{2^{40}} \text{ TiB/second}$ $\frac{11,574.07}{1,099,511,627,776} \approx 1.053 \times 10^{-8} \text{ TiB/second}$

Base-2 (Binary) Conversion

1. Understand the Base Units:

• 1 gigabit (binary) = 2^30 bits
• 1 day = 86,400 seconds (as before)

2. Convert Gigabits per Day to Bits per Second:

1 gibibit/day = (2^30 bits/day) / (86,400 seconds/day)

Calculation: $\frac{2^{30} \text{ bits}}{86,400 \text{ seconds}} \approx 12,207.03 \text{ bits/second}$

3. Convert Bits per Second to Tebibytes per Second:

1 tebibyte (TiB) = 2^40 bits $12,207.03 \text{ bits/second} \approx \frac{12,207.03}{2^{40}} \text{ TiB/second}$ $\frac{12,207.03}{1,099,511,627,776} \approx 1.111 \times 10^{-8} \text{ TiB/second}$

Summary

1 base-10 gigabit per day ≈ 1.053 × 10^-8 TiB/second 1 base-2 gigabit per day ≈ 1.111 × 10^-8 TiB/second

Real-World Examples for Other Quantities of Gigabits Per Day

1. 10 Gigabits per day:

   • Base-10: $10 \times 1.053 \times 10^{-8} = 1.053 \times 10^{-7} \text{ TiB/second}$
   • Base-2: $10 \times 1.111 \times 10^{-8} = 1.111 \times 10^{-7} \text{ TiB/second}$

2. 100 Gigabits per day:

   • Base-10: $100 \times 1.053 \times 10^{-8} = 1.053 \times 10^{-6} \text{ TiB/second}$
   • Base-2: $100 \times 1.111 \times 10^{-8} = 1.111 \times 10^{-6} \text{ TiB/second}$

3. 1 Terabit (1,000 Gigabits) per day:

   • Base-10: $1,000 \times 1.053 \times 10^{-8} = 1.053 \times 10^{-5} \text{ TiB/second}$
   • Base-2: $1,000 \times 1.111 \times 10^{-8} = 1.111 \times 10^{-5} \text{ TiB/second}$

By following these steps, you should be able to convert any given quantity from gigabits per day to tebibytes per second, in both base-10 and base-2 units.