Gibibytes per second to Gibibits per hour conversion

How to convert gibibytes per second to gibibits per hour?

To convert 1 Gibibyte per second (GiB/s) to Gibibits per hour (Gib/h), you need to consider the relationships between these units.

Step-by-Step Conversion

1. Understand the Units:

   • 1 Gibibyte (GiB) is composed of 2^30 bytes.
   • 1 byte is composed of 8 bits.

2. Convert Gibibytes to Bits:

   • 1 GiB = 2^30 bytes
   • 1 byte = 8 bits
   • So, 1 GiB = 2^30 bytes * 8 bits/byte = 2^30 * 8 bits = 2^33 bits

3. Convert Seconds to Hours:

   • 1 second = 1 / 3600 hours
   • Thus, to convert 1 second to hours, you multiply by 3600

4. Calculate the Conversion:

   • Data transfer rate in GiB/s to Gib/h:
   • $\text{Data rate in GiB/s} \times \text{GiBs to bits conversion} \times \text{Seconds to Hours conversion} = \text{Data rate in Gib/h}$
   • $1 \text{ GiB/s} \times 2^{33} \text{ bits/GiB} \times 3600 \text{ s/hour} = 2^{33} \times 3600 \text{ bits/hour}$
   • $2^{33} \times 3600 \text{ bits/hour} \approx 30,869,640,192 \text{ Gib/h}$

So, converting 1 Gibibyte per second to Gibibits per hour: $1 \text{ GiB/s} = 30,869,640,192 \text{ Gib/h}$

Base 10 Explanation

In practice, sometimes data rates use a base 10 interpretation (though it is less common for GiB and Gib units):

1. Convert Base 10 Gibibytes to Base 10 Bits:

   • 1 GiB (base 10) = 10^9 bytes (base 10) * 8 bits/byte = 8 * 10^9 bits

2. Calculate Conversion:

   • Data rate in GiB/s (base 10) to Gib/h (base 10):
   • $1 \text{ GiB/s (base 10)} \times 8 \times 10^9 \text{ bits/GiB} \times 3600 \text{ s/hr} = 8 \times 10^9 \times 3600 \text{ bits/hour}$
   • $8 \times 10^9 \times 3600 \text{ bits/hour} = 28,800 \times 10^9 \text{ bits/hour} = 28,800,000,000,000 \text{ bits/hour}$

So, converting 1 Gibibyte per second (base 10) to "bits per hour" (base 10): $1 \text{ GiB/s (base 10)} = 28,800,000,000,000 \text{ bits/hour}$

Real-world Examples for Other Quantities of GiB/s

1. 10 GiB/s:

   • In binary, converting 10 GiB/s to Gib/h would be:
   • $10 \times 2^{33} \times 3600 \approx 308,696,401,920 \text{ Gib/h}$
   • In base 10, converting 10 GiB/s to bits/hour would be:
   • $10 \times 28,800,000,000,000 \text{ bits/hour} = 288,000,000,000,000 \text{ bits/hour}$

2. 100 GiB/s:

   • In binary, converting 100 GiB/s to Gib/h would be:
   • $100 \times 2^{33} \times 3600 \approx 3,086,964,019,200 \text{ Gib/h}$
   • In base 10, converting 100 GiB/s to bits/hour would be:
   • $100 \times 28,800,000,000,000 \text{ bits/hour} = 2,880,000,000,000,000 \text{ bits/hour}$

3. 0.5 GiB/s:

   • In binary, converting 0.5 GiB/s to Gib/h would be:
   • $0.5 \times 2^{33} \times 3600 \approx 15,434,820,096 \text{ Gib/h}$
   • In base 10, converting 0.5 GiB/s to bits/hour would be:
   • $0.5 \times 28,800,000,000,000 \text{ bits/hour} = 14,400,000,000,000 \text{ bits/hour}$

These conversions illustrate the significant differences between binary and decimal notations within data rates. The base 2 conversions use powers of 2, while the base 10 conversions use powers of 10, leading to different numerical outcomes despite the similarity in unit names.