Convert 10010 to decimal.
Understand the Problem
The question is asking to convert the binary number '10010' into its decimal equivalent. This involves understanding the base-2 numbering system and how to calculate its value based on the position of each digit.
Answer
$18$
Answer for screen readers
The decimal equivalent of the binary number '10010' is $18$.
Steps to Solve
- Identify the binary digits
The given binary number is '10010'. The digits from right to left are:
- $0$ (2^0)
- $1$ (2^1)
- $0$ (2^2)
- $0$ (2^3)
- $1$ (2^4)
- Calculate the decimal value of each binary digit
To convert each binary digit to its decimal value, multiply the digit by $2^{\text{position}}$ where position starts from $0$ on the right:
- $0 \times 2^0 = 0$
- $1 \times 2^1 = 2$
- $0 \times 2^2 = 0$
- $0 \times 2^3 = 0$
- $1 \times 2^4 = 16$
- Sum the decimal values
Now, add all the decimal values calculated for each digit: $$ 0 + 2 + 0 + 0 + 16 = 18 $$
The decimal equivalent of the binary number '10010' is $18$.
More Information
In binary, each digit represents a power of two. The rightmost digit represents $2^0$, the next one $2^1$, and so on. This method of converting binary to decimal is fundamental in computer science and digital electronics.
Tips
- Forgetting to multiply by the correct power of two based on the digit's position.
- Ignoring digits that are '0', which do not contribute to the sum.
