If there are 1026 cities which have to be given a different binary number, then 1026 binary numbers would be needed. It is known that the first number would be 0 so that the highest number would be 1025. For knowing the number of bits to giving each city a different binary number, following steps are required:

Step 1:

Get the number nearest less than the 1025 which could be represented in the form of 2^x.

Step 2:

• 2¹⁰ represents the number 1024. Now, the given formula could be applied: A=2^b. ‘A’ represents the number of alternatives and ‘b’ represents the number of bits.

• It is very clear that if the value of any variable is known then the value of another could be calculated.

• Here, the alternatives are, as considered, 1024. It is the value of variable ‘A’. By put the value: 2¹⁰=2^b. So the value of b (number of bits) is 10.

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