Gibibytes per minute to Kibibytes per hour conversion

How to convert gibibytes per minute to kibibytes per hour?

To convert from Gibibytes per minute (GiB/min) to Kibibytes per hour (KiB/h), we need to understand the relationships between these units in both base 2 (binary) and base 10 (decimal) systems.

1 Gibibyte (GiB) = 2^30 bytes = 1,073,741,824 bytes (base 2) 1 Kibibyte (KiB) = 2^10 bytes = 1,024 bytes (base 2)

1 Gigabyte (GB) = 10^9 bytes = 1,000,000,000 bytes (base 10) 1 Kilobyte (KB) = 10^3 bytes = 1,000 bytes (base 10)

Conversion Using Base 2 (Binary):

1. Convert 1 GiB to bytes: $1 \, \text{GiB} = 2^{30} \, \text{bytes} = 1,073,741,824 \, \text{bytes}$

2. Calculate the number of bytes transferred in one minute: $1 \, \text{GiB/min} = 1,073,741,824 \, \text{bytes/min}$

3. Convert minutes to hours: $1 \, \text{minute} = \frac{1}{60} \, \text{hours}$ Thus, per hour: $\text{Bytes in an hour} = 1,073,741,824 \, \text{bytes} \times 60 \, \text{min/hr} = 64,424,509,440 \, \text{bytes/hr}$

4. Convert bytes to Kibibytes: $1 \, \text{KiB} = 1,024 \, \text{bytes}$ Therefore, $\text{Kibibytes per hour} = \frac{64,424,509,440 \, \text{bytes}}{1,024 \, \text{bytes/KiB}} = 62,914,560 \, \text{KiB/hr}$

Conversion Using Base 10 (Decimal):

1. Convert 1 GB to bytes: $1 \, \text{GB} = 10^9 \, \text{bytes} = 1,000,000,000 \, \text{bytes}$

2. Calculate the number of bytes transferred in one minute: $1 \, \text{GB/min} = 1,000,000,000 \, \text{bytes/min}$

3. Convert minutes to hours: $1 \, \text{minute} = \frac{1}{60} \, \text{hours}$ Thus, per hour: $\text{Bytes in an hour} = 1,000,000,000 \, \text{bytes} \times 60 \, \text{min/hr} = 60,000,000,000 \, \text{bytes/hr}$

4. Convert bytes to Kilobytes: $1 \, \text{KB} = 1,000 \, \text{bytes}$ Therefore, $\text{Kilobytes per hour} = \frac{60,000,000,000 \, \text{bytes}}{1,000 \, \text{bytes/KB}} = 60,000,000 \, \text{KB/hr}$

Summary:

• Using base 2 (binary): 1 GiB/min = 62,914,560 KiB/hr
• Using base 10 (decimal): 1 GB/min = 60,000,000 KB/hr

Real World Examples:

• 2 GiB/min (Base 2): $2 \times 62,914,560 \, \text{KiB/hr} = 125,829,120 \, \text{KiB/hr}$

• 0.5 GiB/min (Base 2): $0.5 \times 62,914,560 \, \text{KiB/hr} = 31,457,280 \, \text{KiB/hr}$

• 5 GiB/min (Base 2): $5 \times 62,914,560 \, \text{KiB/hr} = 314,572,800 \, \text{KiB/hr}$

• 1.5 GiB/min (Base 2): $1.5 \times 62,914,560 \, \text{KiB/hr} = 94,371,840 \, \text{KiB/hr}$

Note: When using base 10, you follow a similar multiplication but convert using the decimal-based constants.