AAB - Abstracted Algorithms (Lesson)

Abstracted Algorithms

Introduction

Now we are going to look at the basic algorithm that creates the zeroes and ones of the internet.  How does that work? Yes, this algorithm is a method that is abstracted (hidden) from us, upper level programmers, but we can understand with small items, how the conversion algorithm works.   Steps to the solution to a problem, the steps to convert from one number system to another is an algorithm.  

In order for us to understand the binary algorithm conversion of the internet, we will first work with the decimal system, the math of our world in the United States.

Decimal System

For example, our numbers are in the decimal or base 10 number system. The numbers from 0 - 9 may be written in every position beginning of base 10. Base 10 positions begin with 10⁰ or the 1's position. Then there is 10¹ which is the 10's position, etc. Examine the table below and see how the numbers in our system are created.  

Note the different exponents on the base. The exponent in a numbering system always begins with 0 and continues upward from there, adding 1 to determine the next place value. Thus the number 120, 529, seen on the top line of the math section, has a 1 in the 100,000's place value indicating 100,000 = 1 * 100,000. In the base 10 numbering system it is easy to find the exponent, just count the number of zeros after the number. 100,000 = 10⁵.  The "how many" value times the "place" always equals the amount.  

Let's try another. The 5 is located in the 100's place value so 5 * 100 = 500.  Add up all of the numbers and we have 120,529, the complete base 10 number.  

The one's position is holding 9 ones, 9 * 1 = 9. What happens if we add 1, 9 + 1 = 10. The one's position becomes zero and the 10's position now holds a 1 because there is a full place value. Thus the numbers allowed in any one place value are the natural numbers less than the base of the system, and for the decimal system these are the numbers 0 - 9. Natural numbers are the counting numbers: 0, 1, 2, 3, 4, etc. on forever.