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ISI 2021 | PCB Mathematics | Question: 1

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Consider a standard balance with two pans where weights can only be placed on the left pan, and the object to be weighed on the right pan. Find the minimum number of weights required to weigh any object whose weight in grams could be any integer ranging from $1$ to $127$. Give precise argument in favor of your answer.
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Any number between 1 to 127 can be represented using 7 bits in binary.

Therefore we need 7 numbers to represent the weight of the 7 bits.

The numbers are : 2^0 = 1,  2^1 = 2,  2^2 = 4,  2^3 = 8,  2^4 = 16,  2^5 = 32,  2^6 = 64.

Ans: 7 numbers required at minimum.
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