Kilobits per hour to Mebibytes per second conversion

How to convert kilobits per hour to mebibytes per second?

Converting data transfer rates involves several steps. Let's start by understanding the units and their conversions:

1. Kilobits per hour (kb/h): A kilobit is $10^3$ bits in the decimal (SI) system and $2^{10}$ bits in the binary (IEC) system.
2. Mebibytes per second (MiB/s): A mebibyte is $2^{20}$ bytes in the binary (IEC) system.

Let's break this down step by step, first for the base 10 system and then for the base 2 system.

Base 10 Conversion (Using the Decimal System)

1. Convert Kilobits to Bits: $1 \text{ kb} = 1 \times 10^3 \text{ bits}$ So, $1 \text{ kb/h} = 1 \times 10^3 \text{ bits per hour}$.

2. Convert Bits to Bytes (since there are 8 bits in a byte): $1 \times 10^3 \text{ bits per hour} \div 8 = 125 \text{ bytes per hour}$

3. Convert Hours to Seconds (since there are 3600 seconds in an hour): $125 \text{ bytes per hour} \div 3600 = 0.03472 \text{ bytes per second}$

4. Convert Bytes to Mebibytes:

   • Note that 1 MiB = $2^{20}$ bytes = 1,048,576 bytes.

   $0.03472 \text{ bytes per second} \div 1,048,576 = 3.313 \times 10^{-8} \text{ MiB/s}$

   Hence, $1 \text{ kb/h}$ is approximately $3.313 \times 10^{-8} \text{ MiB/s}$ in the base 10 system.

Base 2 Conversion (Using the Binary System)

1. Convert Kilobits to Bits: $1 \text{ Kib} = 2^{10} \text{ bits} = 1024 \text{ bits}$ So, $1 \text{ Kib/h} = 1024 \text{ bits per hour}$.

2. Convert Bits to Bytes (8 bits in a byte): $1024 \text{ bits per hour} \div 8 = 128 \text{ bytes per hour}$

3. Convert Hours to Seconds: $128 \text{ bytes per hour} \div 3600 = 0.03556 \text{ bytes per second}$

4. Convert Bytes to Mebibytes:

   • As previously noted, 1 MiB = $2^{20}$ bytes.

   $0.03556 \text{ bytes per second} \div 1,048,576 = 3.392 \times 10^{-8} \text{ MiB/s}$

   So, $1 \text{ Kib/h}$ is approximately $3.392 \times 10^{-8} \text{ MiB/s}$ in the base 2 system.

Real-world Example with Larger Quantities

Let's consider $10^6 \text{ kb/h} = 1,000,000 \text{ kb/h}$.

Base 10 System:

1. Convert Kilobits to Bits: $1,000,000 \times 10^3 \text{ bits}$ So, $1,000,000 \text{ kb/h} = 10^9 \text{ bits per hour}$.

2. Convert Bits to Bytes: $10^9 \text{ bits per hour} \div 8 = 125,000,000 \text{ bytes per hour}$

3. Hours to Seconds: $125,000,000 \text{ bytes per hour} \div 3600 = 34,722.22 \text{ bytes per second}$

4. Bytes to Mebibytes: $34,722.22 \text{ bytes per second} \div 1,048,576 = 0.03312 \text{ MiB/s}$

Base 2 System:

1. Convert Kilobits to Bits: $1,000,000 \times 2^{10} = 1,024,000,000 \text{ bits}$ So, $1,000,000 \text{ Kib/h} = 1,024,000,000 \text{ bits per hour}$.

2. Convert Bits to Bytes: $1,024,000,000 \text{ bits per hour} \div 8 = 128,000,000 \text{ bytes per hour}$

3. Hours to Seconds: $128,000,000 \text{ bytes per hour} \div 3600 = 35,555.56 \text{ bytes per second}$

4. Bytes to Mebibytes: $35,555.56 \text{ bytes per second} \div 1,048,576 = 0.03392 \text{ MiB/s}$

Thus, large quantities like 1,000,000 kb/h show a clear difference in outcomes depending on whether base 10 or base 2 calculations are used.

Summary:

• 1 kb/h ≈ 3.313 × 10^-8 MiB/s (Base 10)
• 1 Kib/h ≈ 3.392 × 10^-8 MiB/s (Base 2)

Real-world example:

• 1,000,000 kb/h ≈ 0.03312 MiB/s (Base 10)
• 1,000,000 Kib/h ≈ 0.03392 MiB/s (Base 2)

This breakdown illustrates how to make the conversions and provides tangible differences between the two systems.