11110000 in decimal
Understand the Problem
The question is asking to convert the binary number 11110000 into its decimal equivalent. This involves calculating the value of each bit in the binary number based on its position and summing those values.
Answer
The decimal equivalent of the binary number $11110000$ is $240$.
Answer for screen readers
The decimal equivalent of the binary number $11110000$ is $240$.
Steps to Solve
- Identify the binary number and its positions
The binary number given is $11110000$. We will assign each bit a value based on its position, starting from the right (0 position):
Position: 7 6 5 4 3 2 1 0
Binary: 1 1 1 1 0 0 0 0
- Calculate the decimal value for each bit
Each position corresponds to a power of 2. We can calculate the decimal value of each bit that is '1'. The values for positions 7 to 4 are:
- Position 7: $1 \cdot 2^7 = 128$
- Position 6: $1 \cdot 2^6 = 64$
- Position 5: $1 \cdot 2^5 = 32$
- Position 4: $1 \cdot 2^4 = 16$
Positions 3 to 0 are all zero, so we will not need to calculate them.
- Sum the calculated values
Now add the values from the bits that are '1':
$$ 128 + 64 + 32 + 16 = 240 $$
The decimal equivalent of the binary number $11110000$ is $240$.
More Information
This conversion is a common task in computer science and digital electronics, where binary numbers are frequently used. Understanding how to convert between binary and decimal is fundamental for programming and problem-solving in these fields.
Tips
- Forgetting to consider the power of 2 for each position.
- Miscounting the positions or misaligning the binary number when converting.
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