You are given a list of binary numbers [110011, 111010, 11011, 1110, 11000, 101010, 11110].You can freely choose any 2 numbers from this list. You have to choose them so that the AND of those 2 numbers is maximized. What is the max AND value possible?
Question
You are given a list of binary numbers [110011, 111010, 11011, 1110, 11000, 101010, 11110].You can freely choose any 2 numbers from this list. You have to choose them so that the AND of those 2 numbers is maximized. What is the max AND value possible?
Solution
To solve this problem, we need to understand how the AND operation works in binary. The AND operation takes two bits and returns 1 if both bits are 1. Otherwise, it returns 0.
Here are the steps to solve the problem:
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Convert all the binary numbers to decimal. This is because it's easier to perform mathematical operations in decimal than in binary. Here are the decimal equivalents of the binary numbers:
- 110011 = 51
- 111010 = 58
- 11011 = 27
- 1110 = 14
- 11000 = 24
- 101010 = 42
- 11110 = 30
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Perform the AND operation on every pair of numbers. The AND operation can be performed in Python using the & operator. For example, the AND of 51 and 58 is 51 & 58 = 50.
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Keep track of the maximum result obtained from the AND operation. This can be done using a variable that is initially set to 0. If the result of an AND operation is greater than the value of this variable, update the variable with the new result.
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After performing the AND operation on every pair of numbers, the value of the variable will be the maximum possible AND value.
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Convert the maximum possible AND value back to binary. This can be done in Python using the bin() function. For example, the binary equivalent of 50 is bin(50) = '0b110010'.
So, the maximum possible AND value is '0b110010' or 50 in decimal.
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