bits per second to Gibibits per day conversion

How to convert bits per second to gibibits per day?

Sure, I'd be happy to help explain how to convert from bits per second (bps) to Gibibits per day (Gib/day), and the difference between using base 10 and base 2.

Conversion Basics

• 1 bit per second (bps) means 1 bit is transferred every second.
• There are 86,400 seconds in a day (24 hours * 60 minutes per hour * 60 seconds per minute).

Base 10 (Decimal) Calculation

In base 10, we use the following:

• 1 Gigabit (Gb) = 1,000,000,000 bits
• 1 day = 86,400 seconds

To find out how many gigabits per day (Gb/day) are in 1 bit per second: $\text{Bits per day} = 1 \text{ bps} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$ $\text{Gigabits per day} = \frac{86,400 \text{ bits/day}}{1,000,000,000 \text{ bits/Gb}} = 0.0000864 \text{ Gb/day}$

Base 2 (Binary) Calculation

In base 2, which is more commonly used in computing, we use the following:

• 1 Gibibit (Gib) = $2^{30}$ bits = 1,073,741,824 bits
• 1 day = 86,400 seconds

To find out how many gibibits per day (Gib/day) are in 1 bit per second: $\text{Bits per day} = 1 \text{ bps} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$ $\text{Gibibits per day} = \frac{86,400 \text{ bits/day}}{1,073,741,824 \text{ bits/Gib}} = 0.0000805 \text{ Gib/day}$

Real World Examples

1. Low-speed dial-up internet: typically around 56 kbps (kilobits per second)

   • Base 10: $56 \times 10^3$ bps ≈ 0.4848 Gb/day = 0.0005659 Gib/day
   • Base 2: $56 \times 1024$ bps ≈ 0.4848 Gb/day = 0.0005220 Gib/day

2. Standard ADSL broadband: around 8 Mbps (megabits per second)

   • Base 10: $8 \times 10^6$ bps ≈ 69.12 Gb/day = 7.1057 Gib/day
   • Base 2: $8 \times (1024^2)$ bps ≈ 69.12 Gb/day = 6.9508 Gib/day

3. Fiber optic internet speed: around 1 Gbps (gigabit per second)

   • Base 10: $1 \times 10^9$ bps ≈ 8,640 Gb/day = 857.471 Gib/day
   • Base 2: $1 \times (1024^3)$ bps ≈ 8,640 Gb/day = 838.8608 Gib/day

Summary

• For low data rates, both base 10 and base 2 conversions yield similar values.
• For higher data rates, the difference between base 10 and base 2 becomes more pronounced due to the differing scales (1,000 vs. 1,024).

Understanding these conversions and differences allows for proper measurement and comparison in computing environments, especially when dealing with large-scale data transfer and storage systems.