bits per second to Gigabits per day conversion

How to convert bits per second to gigabits per day?

Sure! Let's go through the process of converting 1 bit per second (bps) to Gigabits per day. We need to understand the difference between using base 10 and base 2 for these conversions.

Base 10 (Decimal System)

In the decimal system, units of data are scaled by powers of 10:

• 1 Kilobit (Kb) = 1,000 bits (10^3 bits)
• 1 Megabit (Mb) = 1,000 Kilobits = 1,000,000 bits (10^6 bits)
• 1 Gigabit (Gb) = 1,000 Megabits = 1,000,000,000 bits (10^9 bits)

First, calculate the number of seconds in one day: $1 \text{ day} = 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 86,400 \text{ seconds/day}$

So, if the data transfer rate is 1 bps, then in one day: $1 \text{ bps} \times 86,400 \text{ seconds} = 86,400 \text{ bits/day}$

Now convert bits to Gigabits using base 10: $86,400 \text{ bits} \times \frac{1 \text{ Gb}}{1,000,000,000 \text{ bits}} = 0.0000864 \text{ Gb/day}$

Base 2 (Binary System)

In the binary system, units of data are scaled by powers of 2:

• 1 Kibibit (Kib) = 1,024 bits (2^10 bits)
• 1 Mebibit (Mib) = 1,024 Kibibits = 1,048,576 bits (2^20 bits)
• 1 Gibibit (Gib) = 1,024 Mebibits = 1,073,741,824 bits (2^30 bits)

So, using the same number of bits per day:

$86,400 \text{ bits/day}$

Convert bits to Gibibits using base 2: $86,400 \text{ bits} \times \frac{1 \text{ Gib}}{1,073,741,824 \text{ bits}} \approx 0.0000806 \text{ Gib/day}$

Therefore:

• Using base 10, 1 bps equates to 0.0000864 Gb/day.
• Using base 2, 1 bps equates to 0.0000806 Gib/day.

Real-World Examples of Other Data Rates:

• 56 kbps (kilobits per second) - Approximate speed of a traditional dial-up internet connection.

  • In base 10: $56,000 \frac{\text{bits}}{\text{sec}} \times 86,400 \text{ sec/day} \times \frac{1 \text{ Gb}}{1,000,000,000 \text{ bits}} = 4.8384 \text{ Gb/day}$
  • In base 2: $56,000 \frac{\text{bits}}{\text{sec}} \times 86,400 \text{ sec/day} \times \frac{1 \text{ Gib}}{1,073,741,824 \text{ bits}} \approx 4.511 \text{ Gib/day}$

• 1 Mbps (Megabit per second) - Typical speed for broadband internet.

  • In base 10: $1,000,000 \frac{\text{bits}}{\text{sec}} \times 86,400 \text{ sec/day} \times \frac{1 \text{ Gb}}{1,000,000,000 \text{ bits}} = 86.4 \text{ Gb/day}$
  • In base 2: $1,000,000 \frac{\text{bits}}{\text{sec}} \times 86,400 \text{ sec/day} \times \frac{1 \text{ Gib}}{1,073,741,824 \text{ bits}} \approx 80.6 \text{ Gib/day}$

• 1 Gbps (Gigabit per second) - Typical speed for high-speed fiber internet.

  • In base 10: $1,000,000,000 \frac{\text{bits}}{\text{sec}} \times 86,400 \text{ sec/day} \times \frac{1 \text{ Gb}}{1,000,000,000 \text{ bits}} = 86,400 \text{ Gb/day}$
  • In base 2: $1,000,000,000 \frac{\text{bits}}{\text{sec}} \times 86,400 \text{ sec/day} \times \frac{1 \text{ Gib}}{1,073,741,824 \text{ bits}} \approx 80,600 \text{ Gib/day}$

By understanding these conversions, you can evaluate data transfer rates and how much data is transmitted over different periods effectively.