Gigabytes per hour to Kilobits per day conversion

How to convert gigabytes per hour to kilobits per day?

Sure, let's go through the conversion process step-by-step. To convert 1 Gigabyte per hour to Kilobits per day, we need to follow these steps:

1. Convert Gigabytes to Bits: A Gigabyte (GB) can be converted to bits, but we'll convert it to Kilobits (Kb) directly for simplicity.

2. Convert Hours to Days: There are 24 hours in a day.

Now, let's consider both base 10 (decimal) and base 2 (binary) cases.

Base 10 (Decimal System)

1 GB = $10^9$ bytes (1,000,000,000 bytes)

1 byte = 8 bits

1 Kilobit (Kb) = $10^3$ bits (1,000 bits)

Convert 1 Gigabyte to Kilobits:

$1 \text{ GB} = 1 \times 10^9 \text{ bytes}$

$1 \text{ byte} = 8 \text{ bits}$

$1 \text{ GB} = 1 \times 10^9 \text{ bytes} \times 8 \text{ bits per byte} = 8 \times 10^9 \text{ bits}$

$8 \times 10^9 \text{ bits} = \frac{8 \times 10^9 \text{ bits}}{10^3 \text{ bits per Kb}} = 8 \times 10^6 \text{ Kilobits} (Kb)$

Convert Per Hour to Per Day:

$1 \text{ GB per hour} = 8 \times 10^6 \text{ Kilobits per hour}$

$1 \text{ day} = 24 \text{ hours}$

$8 \times 10^6 \text{ Kb per hour} \times 24 \text{ hours per day} = 192 \times 10^6 \text{ Kb per day} = 192,000,000 \text{ Kilobits per day}$

Base 2 (Binary System)

1 GiB (Gibibyte) = $2^{30}$ bytes (1,073,741,824 bytes)

1 byte = 8 bits

1 Kibibit (Kib) = $2^{10}$ bits (1,024 bits)

Convert 1 GiB to Kibibits:

$1 \text{ GiB} = 2^{30} \text{ bytes}$

$1 \text{ byte} = 8 \text{ bits}$

$1 \text{ GiB} = 2^{30} \times 8 \text{ bits} = 2^{33} \text{ bits}$

$2^{33} \text{ bits} = \frac{2^{33} \text{ bits}}{2^{10} \text{ bits per Kib}} = 2^{23} \text{ Kibibits (Kib)}$

Since $2^{23} = 8,388,608$,

$1 \text{ GiB} = 8,388,608 \text{ Kib}$

Convert Per Hour to Per Day:

$1 \text{ GiB per hour} = 8,388,608 \text{ Kib per hour}$

$1 \text{ day} = 24 \text{ hours}$

$8,388,608 \text{ Kib per hour} \times 24 \text{ hours per day} = 201,326,592 \text{ Kib per day}$

Summary:

• 1 GB per hour (Base 10) = 192,000,000 Kilobits per day
• 1 GiB per hour (Base 2) = 201,326,592 Kibibits per day

Real World Examples For Other Quantities:

• Movie Streaming: A standard-definition video typically uses around 1 GB per hour. Following the same calculations in base 10:

  • 1 GB per hour = 192,000,000 Kilobits per day
  • For a high-definition video which might be around 3 to 4 GB per hour, you'd have 576,000,000 to 768,000,000 Kilobits per day.

• Downloading Large Files: If you're downloading a game that's 10 GB and it takes about 1 hour, your download rate is 10 GB per hour:

  • 10 GB per hour = 1,920,000,000 Kilobits per day in base 10.

• Data Centers: A data server might handle 50 GB per hour in a busy environment:

  • 50 GB per hour = 9,600,000,000 Kilobits per day in base 10.

This demonstrates how understanding data transfer rates in different units can be applied to various real-world scenarios from streaming media to large data transfers.