Convert 11110 binary to decimal
Understand the Problem
The question is asking how to convert the binary number 11110 into its decimal equivalent. The binary system is base-2 and we can convert it to decimal by calculating the sum of powers of 2 for each digit.
Answer
$15$
Answer for screen readers
The decimal equivalent of the binary number $11110$ is $15$.
Steps to Solve
- Identify the binary digits and their powers
The binary number we have is $11110$. Each digit represents a power of 2, starting from the right with the power of 0. The powers for the binary number are as follows:
- The first digit (from the right) is $1 \times 2^0$
- The second digit is $1 \times 2^1$
- The third digit is $1 \times 2^2$
- The fourth digit is $1 \times 2^3$
- The fifth digit is $0 \times 2^4$
- Calculate the value for each binary digit
Now we will calculate the value for each digit using the powers of 2:
- For $1 \times 2^0 = 1 \times 1 = 1$
- For $1 \times 2^1 = 1 \times 2 = 2$
- For $1 \times 2^2 = 1 \times 4 = 4$
- For $1 \times 2^3 = 1 \times 8 = 8$
- For $0 \times 2^4 = 0 \times 16 = 0$
- Sum all the values
Now we add all the calculated values together:
$$ 1 + 2 + 4 + 8 + 0 = 15 $$
Thus, the decimal equivalent of the binary number $11110$ is $15$.
The decimal equivalent of the binary number $11110$ is $15$.
More Information
Understanding binary to decimal conversion is foundational in computer science and digital electronics. Each digit in a binary number represents a power of 2, making it a useful numbering system for computing.
Tips
- A common mistake is forgetting to include the '0' digit in the calculation. Always ensure all digits are considered in the sum.
- Another mistake is miscalculating the powers of 2; double-check each power to make sure they are correct.
