Gigabytes per day to Kilobits per hour conversion

How to convert gigabytes per day to kilobits per hour?

Sure, let’s go through the conversion step by step for both base 10 (decimal) and base 2 (binary) measurements.

Step-by-Step Conversion

Base 10 (Decimal)

1. Starting with: 1 Gigabyte per day.

   • In base 10, 1 Gigabyte (GB) = $10^9$ bytes (1,000,000,000 bytes).

2. Convert Gigabytes to Bits.

   • 1 byte = 8 bits.
   • Therefore, 1 GB = $10^9$ bytes $\times$ 8 bits/byte = $8 \times 10^9$ bits.

3. Convert Bits per Day to Bits per Hour.

   • 1 day = 24 hours.
   • Therefore, bits per hour = $\frac{8 \times 10^9 \text{ bits}}{24 \text{ hours}}$.

4. Perform the Division:

   • Bits per hour = $\frac{8 \times 10^9}{24} = 3.333 \times 10^8$ bits/hour.

5. Convert Bits per Hour to Kilobits per Hour.

   • In base 10, 1 Kilobit (Kb) = $10^3$ bits (1,000 bits).
   • Therefore, Kilobits per hour = $\frac{3.333 \times 10^8 \text{ bits/hour}}{10^3 \text{ bits/Kb}} = 3.333 \times 10^5$ Kb/hour.

So, in base 10, 1 Gigabyte per day = $3.333 \times 10^5$ Kilobits per hour.

Base 2 (Binary)

1. Starting with: 1 Gigabyte per day.

   • In base 2, 1 Gigabyte (GiB) = $2^{30}$ bytes (1,073,741,824 bytes).

2. Convert Gigabytes to Bits.

   • 1 byte = 8 bits.
   • Therefore, 1 GiB = $2^{30}$ bytes $\times$ 8 bits/byte = $8 \times 2^{30}$ bits.

3. Convert Bits per Day to Bits per Hour.

   • 1 day = 24 hours.
   • Therefore, bits per hour = $\frac{8 \times 2^{30} \text{ bits}}{24 \text{ hours}}$.

4. Perform the Division:

   • Bits per hour = $\frac{8 \times 2^{30}}{24} = \frac{8 \times 1,073,741,824}{24} = 357,913,941.33$ bits/hour.

5. Convert Bits per Hour to Kilobits per Hour.

   • In base 2, 1 Kibibit (Kibit) = $2^{10}$ bits (1,024 bits).
   • Therefore, Kibibits per hour = $\frac{357,913,941.33 \text{ bits/hour}}{2^{10} \text{ bits/Kibibit}} = 349,525.33$ Kibit/hour.

So, in base 2, 1 Gigabyte per day = 349,525.33 Kibibits per hour.

Real-world Examples

Base 10

• 10 GB per day:

  • $10 \times 3.333 \times 10^5$ Kb/hour = $3.333 \times 10^6$ Kb/hour.

• 50 GB per day:

  • $50 \times 3.333 \times 10^5$ Kb/hour = $1.6665 \times 10^7$ Kb/hour.

• 100 GB per day:

  • $100 \times 3.333 \times 10^5$ Kb/hour = $3.333 \times 10^7$ Kb/hour.

Base 2

• 10 GiB per day:

  • $10 \times 349,525.33$ Kibit/hour = $3,495,253.3$ Kibit/hour.

• 50 GiB per day:

  • $50 \times 349,525.33$ Kibit/hour = $17,476,266.5$ Kibit/hour.

• 100 GiB per day:

  • $100 \times 349,525.33$ Kibit/hour = $34,952,533$ Kibit/hour.

These examples show how different quantities of data, measured in Gigabytes per day, translate into Kilobits per hour in both base 10 and base 2 systems.