Convert 1010 to decimal.
Understand the Problem
The question is asking how to convert the binary number 1010 into its decimal equivalent. This involves understanding the positional value of each digit in the binary system.
Answer
The decimal equivalent of the binary number $1010$ is $10$.
Answer for screen readers
The decimal equivalent of the binary number $1010$ is $10$.
Steps to Solve
- Identify the positions of the binary digits
In binary, each position represents a power of 2, starting from the rightmost digit. For the binary number 1010, the positions are as follows:
- $2^3$ (8)
- $2^2$ (4)
- $2^1$ (2)
- $2^0$ (1)
- Determine the value of each digit
Now we multiply each binary digit by its corresponding power of 2:
- The first digit (from the right) is 0: $0 \times 2^0 = 0 \times 1 = 0$
- The second digit is 1: $1 \times 2^1 = 1 \times 2 = 2$
- The third digit is 0: $0 \times 2^2 = 0 \times 4 = 0$
- The fourth digit is 1: $1 \times 2^3 = 1 \times 8 = 8$
- Sum the values
Now, we add up all the values we calculated:
$$ 0 + 2 + 0 + 8 = 10 $$
- Write the final decimal equivalent
The decimal equivalent of the binary number 1010 is therefore 10.
The decimal equivalent of the binary number $1010$ is $10$.
More Information
When converting from binary to decimal, each binary digit represents a power of 2. The binary numbering system is base-2, while the decimal system is base-10.
Tips
- Forgetting to multiply by the correct power of 2: Make sure to keep track of the powers starting from $0$ on the right.
- Incorrectly adding the values: Double-check your addition to ensure accuracy.
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