Convert 10010 binary to decimal.
Understand the Problem
The question is asking us to convert a binary number, specifically '10010', into its decimal equivalent. To solve this, we will use the method of placing values based on powers of 2.
Answer
$18$
Answer for screen readers
The decimal equivalent of the binary number '10010' is $18$.
Steps to Solve
- Identify Binary Positions
Start by writing down the binary number '10010' with its positions indicated from right to left, which correspond to powers of 2.
Position: 4 3 2 1 0
Binary: 1 0 0 1 0
- Calculate the Value for Each Position
Now, calculate the value of each bit by using the formula $2^{position}$ based on whether there's a 1 or a 0 in that position. Only the positions with a 1 contribute to the final sum.
- 1 at position 4 contributes $1 \times 2^4 = 16$
- 0 at position 3 contributes $0 \times 2^3 = 0$
- 0 at position 2 contributes $0 \times 2^2 = 0$
- 1 at position 1 contributes $1 \times 2^1 = 2$
- 0 at position 0 contributes $0 \times 2^0 = 0$
- Add the Contributions
Now, sum the contributions from the positions with a value:
$$ 16 + 0 + 0 + 2 + 0 = 18 $$
- Final Decimal Equivalent
The decimal equivalent of the binary number '10010' is $18$.
The decimal equivalent of the binary number '10010' is $18$.
More Information
Converting binary to decimal involves understanding how each bit in a binary number corresponds to powers of 2. Each position represents an increasing power from right (0) to left, which is foundational in binary number representation.
Tips
- Forgetting to include the contribution of each position can lead to incorrect results.
- Incorrectly determining the powers of 2, especially when counting positions from right to left.
