Kibibits per day to Gigabytes per hour conversion

How to convert kibibits per day to gigabytes per hour?

Converting 1 Kibibit per day to Gigabytes per hour involves understanding the relationships between these units of measure.

Step 1: Conversion factors

1 Kibibit (Kib) is equal to $2^{10}$ bits, which is 1024 bits (because "kibi" denotes a binary prefix). 1 Byte is equal to 8 bits. 1 Gigabyte (GB) in base 10 (SI) is $10^9$ Bytes. 1 Gigabyte (GiB) in base 2 (binary) is $2^{30}$ Bytes, which is 1073741824 Bytes. 1 day is equal to 24 hours.

Step 2: Convert Kibibits to Bits per Day

$1 \text{ Kibibit per day} = 1 \times 1024 \text{ bits/day}$

Step 3: Convert Bits per Day to Bytes per Day

Since 1 Byte = 8 bits:

$\frac{1 \times 1024 \text{ bits}}{8} = 128 \text{ Bytes/day}$

Step 4: Convert Bytes per Day to Bytes per Hour

$\frac{128 \text{ Bytes}}{24 \text{ hours}} = \frac{128}{24} \approx 5.33333 \text{ Bytes/hour}$

Step 5: Convert Bytes per Hour to Gigabytes (Base 10 and Base 2)

Base 10:

$1 \text{ Gigabyte (GB)} = 10^9 \text{ Bytes}$

$\frac{5.33333 \text{ Bytes/hour}}{10^9 \text{ Bytes/GB}} \approx 5.33333 \times 10^{-9} \text{ GB/hour}$

Base 2:

$1 \text{ Gigabyte (GiB)} = 2^{30} \text{ Bytes} = 1073741824 \text{ Bytes}$

$\frac{5.33333 \text{ Bytes/hour}}{2^{30} \text{ Bytes/GiB}} \approx \frac{5.33333}{1073741824} \approx 4.966 \times 10^{-9} \text{ GiB/hour}$

So:

• In base 10: $1 \text{ Kibibit/day} \approx 5.33333 \times 10^{-9} \text{ GB/hour}$
• In base 2: $1 \text{ Kibibit/day} \approx 4.966 \times 10^{-9} \text{ GiB/hour}$

Real-World Examples for Other Quantities

1. Streaming a Low-Quality Audio (64 Kbps):

   • Kibibits per day: $64 \times 60 \times 60 \times 24 \times 1/1024 \approx 5400 \text{ Kib/day}$
   • This is roughly 0.029 GB/hour in base 10.

2. Downloading a High-Resolution Image (5 MiB):

   • Kibibits per day: If you repeatedly download that image once every hour:
     • $5 \text{ MiB} \times 1024 \times 8 \times 24 / 1024 = 98304 \text{ Kib/day}$
   • This is approximately 0.544 GB/hour in base 10.

3. Daily Data Transfer for a Small Website (~2 GiB):

   • Kibibits per day: 2 GiB/day:
     • $2 \times 2^{30} \times 8 / 1024 \approx 16777216 \text{ Kib/day}$
   • This is about 19.53 GB/hour in base 10.

Hopefully, this gives you a clear understanding of how to convert and interpret these units in real-world scenarios!