Answer
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Step 1:: Recall that in binary, each digit position represents a power of 2.
The rightmost position represents 2^0, the next position to the left represents 2^1, and so on.
Step 2:: To convert the binary number 11111111 to decimal, we need to calculate the sum of the products of each digit and its corresponding power of 2.
Step 3:: Starting from the rightmost digit:
- The 1 in the 2^0 position contributes 2^0 = 1. - The 1 in the 2^1 position contributes 2^1 = 2. - The 1 in the 2^2 position contributes 2^2 = 4. - The 1 in the 2^3 position contributes 2^3 = 8. - The 1 in the 2^4 position contributes 2^4 = 16. - The 1 in the 2^5 position contributes 2^5 = 32. - The 1 in the 2^6 position contributes 2^6 = 64. - The 1 in the 2^7 position contributes 2^7 = 128.
Step 4:: Summing up these contributions, we have:
Final Answer
The binary number 11111111 is equivalent to the decimal number 255.
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