Convert the binary number 11101 to decimal.
Understand the Problem
The question is asking how to convert the binary number 11101 into its decimal equivalent. To solve this, we will use the positional value of each binary digit, which represents powers of 2.
Answer
27
Answer for screen readers
The decimal equivalent of the binary number 11101 is 27.
Steps to Solve
- Identify the binary digits and their positions
Each digit in the binary number represents a power of 2, starting from the rightmost digit. For the binary number 11101, the positions (from right to left) are as follows:
- 0th position: $1$
- 1st position: $1$
- 2nd position: $0$
- 3rd position: $1$
- 4th position: $1$
- Calculate the value of each binary digit
Now, we multiply each digit by its corresponding power of 2:
- $1 \times 2^4 = 1 \times 16 = 16$
- $1 \times 2^3 = 1 \times 8 = 8$
- $0 \times 2^2 = 0 \times 4 = 0$
- $1 \times 2^1 = 1 \times 2 = 2$
- $1 \times 2^0 = 1 \times 1 = 1$
- Sum the values to get the decimal equivalent
Now, we add all the calculated values together:
$$ 16 + 8 + 0 + 2 + 1 = 27 $$
Thus, the decimal equivalent of the binary number 11101 is 27.
The decimal equivalent of the binary number 11101 is 27.
More Information
Converting binary to decimal is a fundamental concept in computer science, as computers use binary (base 2) to represent data. Each binary digit contributes to the overall value based on its position, where each position represents an increasing power of 2.
Tips
- Ignoring powers of 2: Students often forget to multiply the binary digits by the corresponding powers of 2. Always remember to do this step!
- Misadding values: Sometimes students make calculation errors when summing the values. It's important to double-check your addition.
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