Convert binary 11111 to decimal.
Understand the Problem
The question is asking to convert a binary number, specifically 11111, into its decimal (base 10) equivalent. To solve this, we will evaluate the binary digits in terms of powers of 2.
Answer
31
Answer for screen readers
The final answer is 31
Steps to Solve
- Identify the place values of the binary digits
Each digit in a binary number represents a power of 2, starting from the rightmost digit, which is $2^0$, then $2^1$, $2^2$, and so on.
- Multiply each binary digit by its corresponding power of 2
For the binary number 11111:
$$egin{align*} 1 imes 2^4 &= 16 \ 1 imes 2^3 &= 8 \ 1 imes 2^2 &= 4 \ 1 imes 2^1 &= 2 \ 1 imes 2^0 &= 1 \ ext{Sum} &= 16 + 8 + 4 + 2 + 1
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The final answer is 31
More Information
Binary is a base-2 numeral system, meaning it only uses two digits: 0 and 1. The position of each digit represents an increasing power of 2.
Tips
A common mistake is to incorrectly assign the power of 2 to each binary digit. Start from the rightmost digit with $2^0$ and move left, incrementing the exponent by 1 for each position.
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