Gigabytes per month to Gibibits per second conversion

How to convert gigabytes per month to gibibits per second?

Sure! To convert 1 Gigabyte per month (GB/month) to Gibibits per second (Gib/s), we need to follow a series of conversion steps. Here's how you do it:

Conversion factors:

1. 1 Byte (B) = 8 bits (b)
2. 1 Gigabyte (GB) = 10^9 Bytes (base 10)
3. 1 Gibibyte (GiB) = 2^30 Bytes (base 2)
4. 1 Month ≈ 30.44 days (average month considering the Gregorian calendar)
5. 1 Day = 24 hours
6. 1 Hour = 60 minutes
7. 1 Minute = 60 seconds

Base 10 Calculations:

Step 1: Convert GB to bits

1 GB = 10^9 Bytes

1 Byte = 8 bits

So, 1 GB = 10^9 * 8 bits = 8 * 10^9 bits

Step 2: Convert months to seconds

1 Month ≈ 30.44 days 1 Day = 24 hours 1 Hour = 60 minutes 1 Minute = 60 seconds

Total seconds in a month = 30.44 * 24 * 60 * 60 ≈ 2,629,744 seconds

Step 3: Calculate bits per second

1 GB/month = 8 * 10^9 bits / 2,629,744 seconds ≈ 3,042.097 bps (bits per second)

Step 4: Convert to Gibibits per second

1 Gibibit = 2^30 bits

3,042.097 bps * (1 Gib / 2^30 bits) ≈ 2.83 * 10^-6 Gib/s

Base 2 Calculations:

Step 1: Convert GB to GiB

1 GB = 10^9 Bytes

1 GiB = 2^30 Bytes = 1,073,741,824 Bytes

1 GB = 10^9 / 1,073,741,824 GiB ≈ 0.931 GiB

Step 2: Convert GiB to Gibibits

1 GiB = 2^30 Bytes

1 GiB = 2^30 * 8 bits = 8 * 2^30 bits = 2^33 bits

So, 0.931 GiB * 2^33 bits ≈ 7.452 * 10^9 bits

Step 3: Convert months to seconds

(As done before: ≈ 2,629,744 seconds)

Step 4: Calculate bits per second

7.452 * 10^9 bits / 2,629,744 seconds ≈ 2,834 bps

Step 5: Convert to Gibibits per second

2,834 bps * (1 Gib / 2^30 bits) ≈ 2.64 * 10^-6 Gib/s

Real-World Examples

• 50 GB/month:

  • Base 10: $50 * 3,042.097 \approx 152,104.85$ bps ≈ $0.000045 Gib/s$
  • Base 2: $50 * 0.00000264 \approx 0.000132$ Gib/s

• 10 GB/month:

  • Base 10: $10 * 3,042.097 \approx 30,420.97$ bps ≈ $0.000009$ Gib/s
  • Base 2: $10 * 0.00000264 \approx 0.0000264$ Gib/s

• 100 GB/month:

  • Base 10: $100 * 3,042.097 \approx 304,209.7$ bps ≈ $0.000091$ Gib/s
  • Base 2: $100 * 0.00000264 \approx 0.000264$ Gib/s

These differences arise because Gigabyte (GB) uses the base 10 (decimal), while Gibibyte (GiB) uses the base 2 (binary) system.