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## Binary Representation of Numbers

We commonly represent number is base 10, there are 10 elements in our base 10 numbering system, 0,1,2,3,4,5,6,7,8, and 9. In a base n counting system there are n distinct elements, 0 through n - 1.

When a number which is greater than n - 1 needs to be displayed in base n it is represented by a string of the n - 1 elements. The value of any given symbol in the string is found by multiplying that symbol by nx, where x is the number of symbols in the string that are to the right of the symbol in question.

For example, in base 10 the number 982 is equal to 9*102 +8*101 +2*100.

Likewise, in base two the number 10101001 is equal to 1*27 +0*26 +1*25 +0*24 +1*23 +0*22 +0*21 +1*20 = 169 in base 10.

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Matthew Hayward - Quantum Computing and Shor's Algorithm GitHub Repository