Convert 10111 binary to decimal.
Understand the Problem
The question is asking how to convert the binary number 10111 into its decimal equivalent. This involves calculating the value of each binary digit (bit) based on its position and summing them up.
Answer
23
Answer for screen readers
The decimal equivalent of the binary number 10111 is 23.
Steps to Solve
- Identify the place values of the binary digits
In a binary number, each digit represents a power of 2, starting from the right. For the binary number 10111, the place values from right to left are:
- $2^0$ (1)
- $2^1$ (2)
- $2^2$ (4)
- $2^3$ (8)
- $2^4$ (16)
- Break down the binary number into its components
Now, we can break down the binary number 10111 according to its place values:
- The rightmost digit (1) is in the $2^0$ place: $1 \times 2^0 = 1$
- The next digit (1) is in the $2^1$ place: $1 \times 2^1 = 2$
- The next digit (1) is in the $2^2$ place: $1 \times 2^2 = 4$
- The next digit (0) is in the $2^3$ place: $0 \times 2^3 = 0$
- The leftmost digit (1) is in the $2^4$ place: $1 \times 2^4 = 16$
- Sum the results of each digit's contribution
Now we need to sum all the values we calculated:
$$ 1 + 2 + 4 + 0 + 16 = 23 $$
The decimal equivalent of the binary number 10111 is 23.
More Information
When converting binary to decimal, you are essentially calculating the sum of each bit multiplied by its corresponding power of 2. In this case, the binary number 10111 translates to 23 in decimal form.
Tips
- Forgetting to account for the place value of each bit might lead to incorrect contributions.
- Miscalculating the powers of 2 can result in wrong sums.
- Not summing all contributions correctly.
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