Megabits per second to Gibibits per month conversion

How to convert megabits per second to gibibits per month?

To convert 1 Megabit per second (Mbps) to Gibibits per month, it is necessary to understand the units involved and perform the necessary conversions. Note that there are two ways to perform the conversion: using the base 10 (decimal) system and the base 2 (binary) system. We'll consider both methods.

Base 10 (Decimal) Conversion

1 Megabit per second (Mbps) is equal to 1,000,000 bits per second, as per the base 10 system.

Steps:

1. Convert seconds to a month's worth of seconds:

   • There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and approximately 30 days in a month.
   • So, the total number of seconds in a month is: $60 \times 60 \times 24 \times 30 = 2,592,000$ seconds.

2. Calculate the total bits per month:

   • Since 1 Mbps = 1,000,000 bits per second, the total bits in a month: $1,000,000 \times 2,592,000 = 2,592,000,000,000$ bits.

3. Convert bits to Gibibits:

   • 1 Gigabit (Gb) in base 10 is $10^9$ bits.
   • Therefore, to convert bits to Gigabits: $\frac{2,592,000,000,000}{10^9} = 2,592$ Gigabits (Gb).

   But for Gibibits (Gib in base 2):

   • 1 Gibibit = $2^{30} \approx 1,073,741,824$ bits.
   • Therefore, to convert bits to Gibibits: $\frac{2,592,000,000,000}{1,073,741,824} \approx 2,414.29$ Gibibits (Gib).

Base 2 (Binary) Conversion

1 Megabit per second (Mbps) in base 2 is $2^{20}$ bits, which is equal to 1,048,576 bits per second.

Steps:

1. Convert seconds to a month's worth of seconds (same as above):

   • Total seconds in a month: $2,592,000$.

2. Calculate the total bits per month:

   • Since 1 Mbps (in base 2) = 1,048,576 bits per second, the total bits in a month: $1,048,576 \times 2,592,000 \approx 2,719,736,832,000$ bits.

3. Convert bits to Gibibits:

   • 1 Gibibit (Gi) in base 2 is $2^{30} = 1,073,741,824$ bits.
   • Therefore, to convert bits to Gibibits: $\frac{2,719,736,832,000}{1,073,741,824} \approx 2,533.75$ Gibibits (Gib).

Real World Examples:

1. 10 Megabits per second (10 Mbps):

   • Base 10: $2,5920$ Gigabits (Gb) or $24,142.9$ Gibibits (Gib) per month.
   • Base 2: $25,337.5$ Gibibits (Gib) per month.

2. 50 Megabits per second (50 Mbps):

   • Base 10: $12,9600$ Gigabits (Gb) or $120,714.5$ Gibibits (Gib) per month.
   • Base 2: $126,688$ Gibibits (Gib) per month.

3. 100 Megabits per second (100 Mbps):

   • Base 10: $25,9200$ Gigabits (Gb) or $241,429$ Gibibits (Gib) per month.
   • Base 2: $253,375$ Gibibits (Gib) per month.

Understanding these conversions can be very useful for tasks such as estimating monthly data usage limits of internet connections or network planning.