I have weights that weight power of 2 kilograms, like 1, 2, 4, 8, 16,…..kilograms. Which weights
are necessary to weight 213 kilograms?
128, 64, 16, 4, 1
power of 2 closest to 213 ?
2^7 = 128 , leaving 85
2^6 = 64 , leaving 21
2^4 = 16, leaving 5
2^2 = 4, leaving 1
Make use of my chart.
Thank you sm!
To determine which weights are necessary to weigh 213 kilograms using power of 2 kilograms weights, you can use the concept of binary representation.
First, convert the number 213 into binary form. In binary form, 213 is represented as 11010101.
Next, starting from the rightmost digit of the binary representation, check if the corresponding digit is 1. If it is, then you will need the weight corresponding to that position.
Looking at the binary representation of 213, we can see that the digits with 1's in them are at positions 0, 2, 4, 6, and 7.
Now, let's map the positions to their respective weights:
Position 0 corresponds to 2^0 = 1 kilogram
Position 2 corresponds to 2^2 = 4 kilograms
Position 4 corresponds to 2^4 = 16 kilograms
Position 6 corresponds to 2^6 = 64 kilograms
Position 7 corresponds to 2^7 = 128 kilograms
Therefore, the weights necessary to weigh 213 kilograms using power of 2 kilograms weights are:
1 kilogram, 4 kilograms, 16 kilograms, 64 kilograms, and 128 kilograms.