bits per month to Gigabytes per day conversion

How to convert bits per month to gigabytes per day?

To convert from bits per month to gigabytes per day, we need to follow a series of conversions. Here's a step-by-step guide for both base 10 (decimal) and base 2 (binary) computations.

Conversion Steps:

1. Convert bits to bytes:

   • In base 10, 1 byte = 8 bits.
   • In base 2, 1 byte = 8 bits (same conversion factor).

2. Convert bytes to gigabytes:

   • In base 10, 1 gigabyte (GB) = 10^9 bytes.
   • In base 2, 1 gibibyte (GiB) = 2^30 bytes.

3. Convert months to days:

   • Assume an average month length of 30.44 days (considering a year has 365.25 days and dividing by 12 months).

Base 10 (Decimal) Conversion:

1. Convert bits to bytes: $1 \text{ bit} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 0.125 \text{ bytes}$

2. Convert bytes to gigabytes: $0.125 \text{ bytes} \times \frac{1 \text{ gigabyte}}{10^9 \text{ bytes}} = 1.25 \times 10^{-10} \text{ gigabytes}$

3. Convert months to days: $\text{From one month to one day:} \\ 1.25 \times 10^{-10} \text{ gigabytes per month} \times \frac{1}{30.44} \text{ day} \approx 4.11 \times 10^{-12} \text{ gigabytes per day}$

Base 2 (Binary) Conversion:

1. Convert bits to bytes: $1 \text{ bit} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 0.125 \text{ bytes}$

2. Convert bytes to gibibytes: $0.125 \text{ bytes} \times \frac{1 \text{ gibibyte}}{2^{30} \text{ bytes}} = 1.164153218 \times 10^{-10} \text{ gibibytes}$

3. Convert months to days: $\text{From one month to one day:} \\ 1.164153218 \times 10^{-10} \text{ gibibytes per month} \times \frac{1}{30.44 \text{ days}} \approx 3.824 \times 10^{-12} \text{ gibibytes per day}$

Real-World Examples:

Let's look at some other quantities to gain perspective on the size:

1. 1 Mbps (megabits per second):

   • In one month: $1 \text{ Mbps} \times 60 \times 60 \times 24 \times 30.44 = 2.56 \times 10^{12} \text{ bits per month}$
   • Converted to gigabytes per day using base 10: $11.742 \text{ GB/day}$
   • Converted to gibibytes per day using base 2: $10.936 \text{ GiB/day}$

2. Typical Broadband Connection (25 Mbps):

   • In one month: $25 \text{ Mbps} \times 60 \times 60 \times 24 \times 30.44 = 64 \times 10^{12} \text{ bits per month}$
   • Converted to gigabytes per day using base 10: $293.56 \text{ GB/day}$
   • Converted to gibibytes per day using base 2: $273.4 \text{ GiB/day}$

3. Large Data Transfer (1 TB per month):

   • 1 terabyte is $10^{12}$ bytes in base 10 or $2^{40}$ bytes in base 2.
   • Converted to bits: $8 \times 10^{12} \text{ bits per month (base 10)}$, $8 \times 2^{40} \text{ bits per month (base 2)}$
   • Per day in base 10: $32.85 \text{ GB/day}$
   • Per day in base 2: $29.93 \text{ GiB/day}$

These examples illustrate the significant differences in scale that can result from using different bases for conversion, as well as highlight the massive amounts of data transferred in modern digital contexts.