11000 binary to decimal
Understand the Problem
The question is asking for the conversion of the binary number 11000 into its decimal equivalent. This involves interpreting the binary digits in relation to their positional values in base 2.
Answer
$24$
Answer for screen readers
The decimal equivalent of the binary number $11000$ is $24$.
Steps to Solve
- Identify the binary digits
The binary number given is $11000$. It has 5 digits: $1$, $1$, $0$, $0$, and $0$.
- Assign positional values
Each binary digit has a positional value based on powers of 2, starting from the right (0). The positional values for the digits, from right to left, are:
- $2^0 = 1$
- $2^1 = 2$
- $2^2 = 4$
- $2^3 = 8$
- $2^4 = 16$
- Calculate the decimal equivalent
Multiply each binary digit by its corresponding positional value:
- The first digit (from the right, which is $0$) contributes $0 \times 2^0 = 0$
- The second digit ($0$) contributes $0 \times 2^1 = 0$
- The third digit ($0$) contributes $0 \times 2^2 = 0$
- The fourth digit ($1$) contributes $1 \times 2^3 = 8$
- The fifth digit ($1$) contributes $1 \times 2^4 = 16$
Now we add these contributions together:
$$ 0 + 0 + 0 + 8 + 16 = 24 $$
- Write the final answer
The decimal equivalent of the binary number $11000$ is $24$.
The decimal equivalent of the binary number $11000$ is $24$.
More Information
The process of converting a binary number to decimal involves using powers of 2. Each digit's position represents a power of 2, and only those positions with a $1$ contribute to the total value. In this case, the binary number $11000$ represents $16 + 8 = 24$ in decimal.
Tips
- Forgetting to assign powers correctly: Ensure you start from $2^0$ for the rightmost digit and move left.
- Incorrectly multiplying by $0$: Remember, any digit multiplied by $0$ will always contribute $0$.
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