Gigabytes per minute to Kilobits per hour conversion

How to convert gigabytes per minute to kilobits per hour?

To convert from Gigabytes per minute (GB/min) to Kilobits per hour (Kb/hr), we need to go through a series of conversions, taking into account the differences in base 10 (decimal) and base 2 (binary) measurements, as they yield different results.

Base 10 (Decimal)

1 Gigabyte (GB) in base 10 is defined as $10^9$ bytes.

1 byte = 8 bits.

1 Kilobit (Kb) = $10^3$ bits.

Step-by-step conversion:

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

2. Convert bytes to bits: $10^9 \text{ bytes} \times 8 \text{ bits/byte} = 8 \times 10^9 \text{ bits}$

3. Convert bits to Kilobits: $8 \times 10^9 \text{ bits} \div 10^3 \text{ bits/Kb} = 8 \times 10^6 \text{ Kb}$

4. Convert per minute to per hour: $8 \times 10^6 \text{ Kb/min} \times 60 \text{ min/hr} = 4.8 \times 10^8 \text{ Kb/hr}$

So, $1 \text{ GB/min} = 480,000,000 \text{ Kb/hr}$ in base 10.

Base 2 (Binary)

1 Gibibyte (GiB) in base 2 is defined as $2^{30}$ bytes.

1 byte = 8 bits.

1 Kibibit (Kib) = $2^{10}$ bits.

Step-by-step conversion:

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

2. Convert bytes to bits: $2^{30} \text{ bytes} \times 8 \text{ bits/byte} = 8 \times 2^{30} \text{ bits}$

3. Convert bits to Kibibits: $8 \times 2^{30} \text{ bits} \div 2^{10} \text{ bits/Kib} = 8 \times 2^{20} \text{ Kib}$

4. Simplify $8 \times 2^{20}$: $8 \times 2^{20} = 8,388,608 \text{ Kib}$

5. Convert per minute to per hour: $8,388,608 \text{ Kib/min} \times 60 \text{ min/hr} = 503,316,480 \text{ Kib/hr}$

So, $1 \text{ GiB/min} = 503,316,480 \text{ Kib/hr}$ in base 2.

Real-world Examples of Other Quantities

5 GB/min (Base 10)

1. Convert to Kb/min: $5 \text{ GB/min} = 5 \times 8 \times 10^6 \text{ Kb/min} = 40 \times 10^6 \text{ Kb/min}$

2. Convert per minute to per hour: $40 \times 10^6 \text{ Kb/min} \times 60 \text{ min/hr} = 2.4 \times 10^9 \text{ Kb/hr}$

So, $5 \text{ GB/min} = 2.4 \times 10^9 \text{ Kb/hr}$.

10 GiB/min (Base 2)

1. Convert to Kib/min: $10 \text{ GiB/min} = 10 \times 8,388,608 \text{ Kib/min} = 83,886,080 \text{ Kib/min}$

2. Convert per minute to per hour: $83,886,080 \text{ Kib/min} \times 60 \text{ min/hr} = 5,033,164,800 \text{ Kib/hr}$

So, $10 \text{ GiB/min} = 5,033,164,800 \text{ Kib/hr}$.

These conversions can be useful in various contexts, such as network data transfer, storage calculations, and understanding the capacity of data handling in information technology systems.