Question

How many bits are required to represent all the elements currently in the Periodic Table?

Answer 1

• Below is the detailed solution of the above mentioned problem.
• Answer: Total number of bits required to represent all the elements currently in the periodic table is 7.
• Total number of elements currently in periodic table are 118, from atomic number 1 i.e, hydrogen to atomic number 118 i.e, Oganesson.
• These 118 elements are discovered and synthesized and these are confirmed by the governing organization IUPAC i.e, International Union of Pure and Applied Chemistry.
• Now we know that to represent x numbers we need floor(log₂x)+1 bits.

As we know that using 1 bit we can represent 2 numbers , using 2 bits we can represent 4 numbers , using 3 bits we can represent 8 numbersand so on. So n number of bits can represent 2ⁿ numbers.

For example we have 3 bits now _ _ _ ( a single bit represented as _ ) , these 3 bits can be filled with 0 or a 1. so by principle of counting we have 222 unique representations using these 3 bits and same goes for other.

Now we know that some n bits can represent 2ⁿ numbers so what we want is to calculate the minimum n for which 2ⁿ 118, so we get answer as 7. As 2⁷=128 which is greater than 118 and 2⁶ = 64 is less than 118.

Or you can use the formula mentioned above which is derived by taking log₂() both sides.

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