Gibibits per minute to Terabits per day conversion

How to convert gibibits per minute to terabits per day?

To convert 1 Gibibit per minute (1 Gi/min) to Terabits per day (Tb/day), we'll walk through the conversion process. We'll need to account for the number of minutes in a day and the difference in binary versus decimal definitions.

Base 2 (Binary) Conversions:

1 Gibibit (Gi) = $2^{30}$ bits = 1,073,741,824 bits

1 day = 24 hours * 60 minutes = 1,440 minutes

First, convert 1 Gi/min to bits per minute: 1 Gi/min = 1,073,741,824 bits per minute

Next, convert to bits per day: = $1,073,741,824 \text{ bits/min} \times 1,440 \text{ min/day}$ = $1,546,171,356,160 \text{ bits/day}$

Now, convert bits per day to Terabits per day where: 1 Terabit (Tb) = $10^{12}$ bits (decimals) or $2^{40}$ bits (binary)

Base 2 Terabits:

1 Tb = $2^{40}$ bits = 1,099,511,627,776 bits

Convert the bits per day to base-2 Terabits: $\frac{1,546,171,356,160 \text{ bits/day}}{1,099,511,627,776 \text{ bits/Tb}}$ $\approx 1.407 \text{ Tb/day}$

Base 10 (Decimal) Conversions:

1 Gibibit (Gi) = 1,073,741,824 bits

1 day = 24 hours * 60 minutes = 1,440 minutes

First, convert 1 Gi/min to bits per minute: 1 Gi/min = 1,073,741,824 bits per minute

Next, convert to bits per day: = $1,073,741,824 \text{ bits/min} \times 1,440 \text{ min/day}$ = $1,546,171,356,160 \text{ bits/day}$

Now, convert bits per day to Terabits per day (where 1 Terabit = $10^{12}$ bits):

Base 10 Terabits:

$\frac{1,546,171,356,160 \text{ bits/day}}{10^{12} \text{ bits/Tb}}$ $= 1.546 \text{ Tb/day}$

Summary:

• Base 2 Terabits: 1 Gi/min = 1.407 Tb/day
• Base 10 Terabits: 1 Gi/min = 1.546 Tb/day

Real-World Examples

Let's apply this to some other quantities of Gibibits per minute:

Example 1: 5 Gibibits per minute

Base 2:

• Bits per minute: 5 * 1,073,741,824 = 5,368,709,120 bits/min
• Bits per day: 5,368,709,120 * 1,440 = 7,730,856,780,800 bits/day
• Base 2 Terabits: $\frac{7,730,856,780,800}{1,099,511,627,776}$ ≈ 7.037 Tb/day

Base 10:

• Bits per minute: 5 * 1,073,741,824 = 5,368,709,120 bits/min
• Bits per day: 5,368,709,120 * 1,440 = 7,730,856,780,800 bits/day
• Base 10 Terabits: $\frac{7,730,856,780,800}{10^{12}}$ = 7.731 Tb/day

Example 2: 100 Gibibits per minute

Base 2:

• Bits per minute: 100 * 1,073,741,824 = 107,374,182,400 bits/min
• Bits per day: 107,374,182,400 * 1,440 = 154,617,135,616,000 bits/day
• Base 2 Terabits: $\frac{154,617,135,616,000}{1,099,511,627,776}$ ≈ 140.704 Tb/day

Base 10:

• Bits per minute: 100 * 1,073,741,824 = 107,374,182,400 bits/min
• Bits per day: 107,374,182,400 * 1,440 = 154,617,135,616,000 bits/day
• Base 10 Terabits: $\frac{154,617,135,616,000}{10^{12}}$ = 154.617 Tb/day