The decimal equivalent of the binary number 1010 is 10.
Understanding the relationship between binary and decimal numbers is fundamental in computer science and digital systems. Binary numbers, which consist of only two digits (0 and 1), are the native language of computers, while decimal numbers are the base-10 system we use in everyday life. Converting between these bases is a common operation.
How to Convert Binary to Decimal
To convert a binary number to its decimal equivalent, you multiply each digit by the power of 2 corresponding to its position, starting from the rightmost digit with 20. Then, you sum the results.
Let's illustrate this with the binary number 1010:
- 1010: The leftmost '1' is in the 23 position (8s place).
- 1010: The next '0' is in the 22 position (4s place).
- 1010: The next '1' is in the 21 position (2s place).
- 1010: The rightmost '0' is in the 20 position (1s place).
The calculation is as follows:
(1 × 23) + (0 × 22) + (1 × 21) + (0 × 20)
= (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1)
= 8 + 0 + 2 + 0
= 10
Common 4-Bit Binary Numbers and Their Decimal Equivalents
Many binary numbers are used in various computing contexts. Here's a quick reference for some 4-bit binary numbers and their corresponding decimal values, showcasing how 1010 fits within this sequence:
| Binary Number | Decimal Equivalent |
|---|---|
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
This table highlights the direct relationship between these common binary patterns and their decimal interpretations, which is crucial for tasks like network addressing, data representation, and digital circuit design. For a more comprehensive overview of this conversion process, you can explore resources on Binary to Decimal Conversion.
