Gigabits per hour to Kibibytes per month conversion

How to convert gigabits per hour to kibibytes per month?

Sure, I'd be happy to explain how to convert 1 Gigabit per hour to Kibibytes per month and illustrate the differences between base 10 (decimal) and base 2 (binary) calculations.

Conversion Steps

Step 1: Gigabits to Bits

1 Gigabit (Gb) = $10^9$ bits (base 10) 1 Gigabit (Gi) = $2^{30}$ bits (base 2)

Step 2: Bits to Bytes

1 Byte = 8 bits

Step 3: Bytes to Kibibytes

1 Kibibyte (KiB) = $2^{10}$ Bytes = 1024 Bytes (base 2) 1 Kilobyte (KB) = $10^3$ Bytes = 1000 Bytes (base 10)

Step 4: Hours to Month

Assume an average month is 30 days, which is 30 x 24 = 720 hours.

Base 10 (Decimal System)

1. Convert 1 Gigabit per hour to bits per hour:

$1 \text{ Gb/hour} = 10^9 \text{ bits/hour}$

2. Convert bits per hour to bytes per hour:

$10^9 \text{ bits/hour} \div 8 = 1.25 \times 10^8 \text{ bytes/hour}$

3. Convert bytes per hour to kilobytes per hour:

$1.25 \times 10^8 \text{ bytes/hour} \div 1000 = 1.25 \times 10^5 \text{ kilobytes/hour}$

4. Convert kilobytes per hour to kilobytes per month:

$1.25 \times 10^5 \text{ kilobytes/hour} \times 720 \text{ hours/month} = 9 \times 10^7 \text{ kilobytes/month}$

Base 2 (Binary System)

1. Convert 1 Gibibit per hour to bits per hour:

$1 \text{ Gibibit/hour} = 2^{30} \text{ bits/hour} = 1073741824 \text{ bits/hour}$

2. Convert bits per hour to bytes per hour:

$1073741824 \text{ bits/hour} \div 8 = 134217728 \text{ bytes/hour}$

3. Convert bytes per hour to Kibibytes per hour:

$134217728 \text{ bytes/hour} \div 1024 = 131072 \text{ Kibibytes/hour}$

4. Convert Kibibytes per hour to Kibibytes per month:

$131072 \text{ Kibibytes/hour} \times 720 \text{ hours/month} = 94371840 \text{ Kibibytes/month}$

Summary

• Base 10:

  • 1 Gigabit per hour = 90,000,000 Kilobytes per month (or 90,000,000 KB/month)

• Base 2:

  • 1 Gigibit per hour = 94,371,840 Kibibytes per month (or 94,371,840 KiB/month)

Real World Examples

1. Streaming HD Video:

   • Typical streaming rates for HD video are around 5 Mbps (Megabits per second).
   • Converting: 5 Mbps * 3600 seconds/hour = 18,000 Mbps/hour = 18 Gbps/hour.
   • Using our conversion: In base 10, $18 \times 90,000,000 = 1,620,000,000$ KB/month.
   • In base 2, $18 \times 94,371,840 = 1,698,693,120$ KiB/month.

2. Online Backup Services:

   • Assume a service uploads data at a rate of 500 Mbps.
   • Converting: 500 Mbps * 3600 seconds/hour = 1,800,000 Mbps/hour = 1,800 Gbps/hour.
   • Using our conversion: In base 10, $1800 \times 90,000,000 = 162,000,000,000$ KB/month.
   • In base 2, $1800 \times 94,371,840 = 169,869,312,000$ KiB/month.

By understanding these conversions and the differences between base 10 and base 2 calculations, you can better estimate data storage and transfer needs for various applications.