Convert 10110 to decimal.
Understand the Problem
The question is asking how to convert the binary number 10110 into its decimal equivalent. This process involves understanding binary numbering and converting it through powers of 2.
Answer
$22$
Answer for screen readers
The decimal equivalent of the binary number 10110 is $22$.
Steps to Solve
-
Identify the binary number We start with the binary number 10110.
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Assign powers of 2 to each digit
Starting from the rightmost digit (least significant bit), assign powers of 2. The rightmost digit corresponds to $2^0$, the next to $2^1$, and so on:
[ \begin{align*} 1 & \quad (2^4)\ 0 & \quad (2^3)\ 1 & \quad (2^2)\ 1 & \quad (2^1)\ 0 & \quad (2^0)\ \end{align*} ]
So, we have:
- $1 \times 2^4$
- $0 \times 2^3$
- $1 \times 2^2$
- $1 \times 2^1$
- $0 \times 2^0$
- Calculate each term Now calculate the value of each digit multiplied by the corresponding power of 2:
[ \begin{align*} 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\ \end{align*} ]
- Sum the calculated values Now, add all these values together:
$$ 16 + 0 + 4 + 2 + 0 = 22 $$
The decimal equivalent of the binary number 10110 is $22$.
More Information
When converting binary numbers, each digit's position represents a power of 2. The rightmost digit is the least significant, and the leftmost is the most significant. This method can be used to convert any binary number to decimal.
Tips
Common mistakes include forgetting to apply the power of 2 correctly or miscalculating the addition of the terms. To avoid this, double-check the powers assigned to each digit and ensure all terms are added accurately.
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