The binary representation of 10 is 1010.
Understanding Binary Representation
The binary system is a base-2 numeral system, meaning it uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from the rightmost digit as 20, then 21, 22, and so on.
To convert the decimal number 10 to binary, we can break it down into powers of 2:
- 10 = (1 x 23) + (0 x 22) + (1 x 21) + (0 x 20)
- 10 = (1 x 8) + (0 x 4) + (1 x 2) + (0 x 1)
Therefore, the binary representation is formed by the coefficients of the powers of 2: 1010.
Conversion Example
Here's a table illustrating how the binary number 1010 corresponds to the decimal number 10:
| Binary Digit | Place Value (Power of 2) | Decimal Value |
|---|---|---|
| 1 | 23 = 8 | 8 |
| 0 | 22 = 4 | 0 |
| 1 | 21 = 2 | 2 |
| 0 | 20 = 1 | 0 |
| Total | 10 |
In Summary
Converting the decimal number 10 to binary involves expressing it as a sum of powers of 2. The binary representation is then formed by the coefficients of those powers, resulting in 1010.
