Convert 10110 binary to decimal.
Understand the Problem
The question is asking how to convert the binary number 10110 into its decimal equivalent. This involves interpreting the binary digits according to their positional values.
Answer
The decimal equivalent of the binary number $10110$ is $22$.
Answer for screen readers
The decimal equivalent of the binary number $10110$ is $22$.
Steps to Solve
- Identify the position of each digit In the binary number $10110$, list each digit from right to left with its positional power of 2. The rightmost digit represents $2^0$, the next one $2^1$, and so on:
Position: 4 3 2 1 0
Digits: 1 0 1 1 0
- Calculate the value of each digit Now, calculate the decimal value for each binary digit using the formula $digit \times 2^{position}$.
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $0 \times 2^0 = 0$
- Sum the values Add all the values calculated in the previous step to find the total decimal value:
$$ 16 + 0 + 4 + 2 + 0 = 22 $$
The decimal equivalent of the binary number $10110$ is $22$.
More Information
Converting binary to decimal involves understanding positional values, where each digit represents an increasing power of 2 from right to left. This conversion is fundamental in computer science since computers operate using binary.
Tips
- Ignoring positional values: Sometimes, students forget to account for the position of each digit, leading to incorrect calculations.
- Calculating incorrectly for higher powers: It's essential to correctly compute the power of 2 for each digit, particularly for the left-most digits where the values are larger.
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