Convert 11101 from binary to decimal.
Understand the Problem
The question is asking to convert the binary number 11101 into its decimal equivalent. To do this, we will take each digit of the binary number, multiply it by 2 raised to the power of its position (counting from right to left starting at 0), and sum these values.
Answer
29
Answer for screen readers
The decimal equivalent of the binary number 11101 is 29.
Steps to Solve
- Identify the binary number positions
The binary number is 11101. We will identify the positions of each digit from right (0) to left.
- Position 0: 1
- Position 1: 0
- Position 2: 1
- Position 3: 1
- Position 4: 1
- Calculate the contribution of each digit
For each digit, we multiply the digit by $2$ raised to the power of its position.
- For position 0: $1 \times 2^0 = 1 \times 1 = 1$
- For position 1: $0 \times 2^1 = 0 \times 2 = 0$
- For position 2: $1 \times 2^2 = 1 \times 4 = 4$
- For position 3: $1 \times 2^3 = 1 \times 8 = 8$
- For position 4: $1 \times 2^4 = 1 \times 16 = 16$
- Sum the contributions
Now, let's add up all the contributions from each digit:
$$ 1 + 0 + 4 + 8 + 16 = 29 $$
The decimal equivalent of the binary number 11101 is 29.
More Information
When converting binary to decimal, you are effectively expressing the binary number in base 2, and the final result is in base 10, which is the standard number system we usually use.
Tips
- Forgetting to include the contribution of the digit at position 1 (which is 0 in this case).
- Incorrectly calculating the power of 2, especially for higher positions.
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