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ISI 2021 | PCB CS | 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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The question is pretty straightforward.
We reduce the problem to "represent any decimal number from 1 to 127 in form of binary number but how many bits do we need to do that?"
That is, ceil(lg 127)=7

Thus, we need, 1, 2, 4, 8, 16, 32, and 64 gram weights
so 7 weights in total we need to represent any number from 1 to 127
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