Kibibits per day to Mebibytes per second conversion

How to convert kibibits per day to mebibytes per second?

Sure, let's go through the conversion step by step. To convert 1 Kibibit per day to Mebibytes per second, we'll need to understand the definitions and then the conversion process. Here's how to break it down:

Definitions

• Kibibit (Kibit): 1 Kibibit = 2^10 bits = 1024 bits
• Mebibyte (MiB): 1 Mebibyte = 2^20 bytes = 1024^2 bytes = 1,048,576 bytes
• Day to Seconds: 1 Day = 24 hours = 24 * 3600 seconds = 86,400 seconds

Since you mentioned that the answer could differ for base 10 and base 2, I will clarify that the terms Kibibit and Mebibyte are inherently base 2 units. However, for clarity, I will explain the conversion as it applies to these units and contrast them slightly with their base 10 counterparts.

Conversion Steps

Step 1: Convert Kibibits per day to bits per second

1 Kibibit/day = 1024 bits/day

Since there are 86,400 seconds in a day: $\text{Bits per second} = \frac{1024 \text{ bits}}{86,400 \text{ seconds}} \approx 0.01185 \text{ bits/second}$

Step 2: Convert bits per second to Mebibytes per second

Now, we need to convert this to bytes per second, and then to Mebibytes per second:

1 Byte = 8 bits

So, $\text{Bytes per second} = \frac{0.01185 \text{ bits/second}}{8} \approx 0.001481 \text{ Bytes/second}$

To convert from bytes per second to Mebibytes per second: $\text{Mebibytes per second} = \frac{0.001481 \text{ Bytes/second}}{1,048,576} \approx 1.41 \times 10^{-9} \text{ MiB/s}$

Contrast with Base 10

In base 10 definitions (often used in networking):

• Kilobit (Kbit): 1 Kilobit = 10^3 bits = 1000 bits
• Megabyte (MB): 1 Megabyte = 10^6 bytes = 1,000,000 bytes

However, since we're dealing with Kibibit and Mebibyte (base 2 units)—if you want base 10 conversions—you'll need to use kilobits and megabytes with the same approach.

Real-world Examples

• 10 Kibibits per day: $\text{Bits per second} = \frac{10 \times 1024 \text{ bits}}{86,400 \text{ seconds}} = 0.1185 \text{ bits/second}$ $\text{Mebibytes per second} = \frac{0.1185}{8} = 0.01481 \text{ Bytes/second}$ $\approx 1.41 \times 10^{-8} \text{ MiB/s}$

• 100 Kibibits per day: $\text{Bits per second} = \frac{100 \times 1024 \text{ bits}}{86,400 \text{ seconds}} = 1.185 \text{ bits/second}$ $\text{Mebibytes per second} = \frac{1.185}{8} = 0.148 \text{ Bytes/second}$ $\approx 1.41 \times 10^{-7} \text{ MiB/s}$

• 1 Megabit per day: $\text{Bits per second} = \frac{1,000,000 \text{ bits}}{86,400 \text{ seconds}} = 11.574 \text{ bits/second}$ $\text{Mebibytes per second} = \frac{11.574}{8 \times 1,048,576} \approx 1.378 \times 10^{-6} \text{ MiB/s}$

These examples highlight how small the data transfer rate is when measured in Mebibytes per second for Kibibits per day.