Bytes to Kilobits conversion

How to convert bytes to kilobits?

To convert bytes to kilobits, we need to recognize that one byte is equal to 8 bits. The distinction you mentioned between base 10 (decimal) and base 2 (binary) systems is crucial for the conversion to kilobits.

Base 10 (Decimal)

In the decimal system, one kilobit (kb) is equivalent to 1000 bits. 1 byte = 8 bits Therefore: $\text{1 byte} = \frac{8 \text{ bits}}{1000 \text{ bits/kilobit}} = 0.008 \text{ kilobits (decimal)}$

Base 2 (Binary)

In the binary system, one kibibit (Kib) is equivalent to 1024 bits. 1 byte = 8 bits Therefore: $\text{1 byte} = \frac{8 \text{ bits}}{1024 \text{ bits/kibibit}} = 0.0078125 \text{ kibibits (binary)}$

Real-World Examples with Different Quantities of Bytes

1. 1 Kilobyte (KB) = 1024 Bytes (Binary)

   • Decimal: 1024 bytes = 1024 * 8 bits = 8192 bits $\text{8192 bits} = \frac{8192}{1000} = 8.192 \text{ kilobits (decimal)}$
   • Binary: 1024 bytes = 1024 * 8 bits = 8192 bits $\text{8192 bits} = \frac{8192}{1024} = 8 \text{ kibibits (binary)}$

2. 1 Megabyte (MB) = 1024 Kilobytes = 1024 * 1024 Bytes (Binary)

   • Decimal: 1,048,576 bytes = 1,048,576 * 8 bits = 8,388,608 bits $\text{8,388,608 bits} = \frac{8388608}{1000} = 8388.608 \text{ kilobits (decimal)}$
   • Binary: 1,048,576 bytes = 1,048,576 * 8 bits = 8,388,608 bits $\text{8,388,608 bits} = \frac{8388608}{1024} = 8192 \text{ kibibits (binary)}$

3. 5 Gigabytes (GB) = 5 * 1024 Megabytes = 5 * 1024 * 1024 Kilobytes = 5 * 1024 * 1024 * 1024 Bytes (Binary)

   • Decimal: 5,368,709,120 bytes = 5,368,709,120 * 8 bits = 42,949,672,960 bits $\text{42,949,672,960 bits} = \frac{42949672960}{1000} = 42,949,672.96 \text{ kilobits (decimal)}$
   • Binary: 5,368,709,120 bytes = 5,368,709,120 * 8 bits = 42,949,672,960 bits $\text{42,949,672,960 bits} = \frac{42949672960}{1024} = 41,943,04 \text{ kibibits (binary)}$

These examples should give you a clear understanding of how to convert bytes to kilobits and the differences between base 10 and base 2 conversions.