Convert 11110000 to decimal.
Understand the Problem
The question is asking to convert the binary number 11110000 into its decimal equivalent. This involves calculating the value of the binary digits in powers of 2.
Answer
$240$
Answer for screen readers
The decimal equivalent of the binary number $11110000$ is $240$.
Steps to Solve
- Identify the binary digits and their positions
The binary number is $11110000$. Here are the positions (from right to left):
- Position 0: 0
- Position 1: 0
- Position 2: 0
- Position 3: 0
- Position 4: 1
- Position 5: 1
- Position 6: 1
- Position 7: 1
- Calculate the decimal value of each binary digit
Each binary digit has a value based on its position. The value of each digit can be calculated using the formula $2^{\text{position}}$:
- Position 0: $0 \times 2^0 = 0$
- Position 1: $0 \times 2^1 = 0$
- Position 2: $0 \times 2^2 = 0$
- Position 3: $0 \times 2^3 = 0$
- Position 4: $1 \times 2^4 = 16$
- Position 5: $1 \times 2^5 = 32$
- Position 6: $1 \times 2^6 = 64$
- Position 7: $1 \times 2^7 = 128$
- Sum the decimal values
Now we sum all the values calculated:
$$ \text{Total} = 0 + 0 + 0 + 0 + 16 + 32 + 64 + 128 = 240 $$
The decimal equivalent of the binary number $11110000$ is $240$.
More Information
When converting from binary to decimal, the leftmost digit represents the highest value (in this case, $2^7$ or 128), while the rightmost digit represents the lowest value ($2^0$ or 1). Each position contributes to the total sum based on whether it is a 0 or a 1.
Tips
- Misreading the binary positions can lead to incorrect calculations. Always count from the right, starting at 0.
- Forgetting to multiply by the powers of 2 can result in missing contributions from certain digits.
