How The Binary Code Works

Binary code is based on an exponential model of multiplication. The code can be used to define an infinitely large exact number to an infinite amount of decimal places. It can do this because the code itself can go on for as long as it needs to.It is arranged as follows:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4098, 8196, 16392, 32784.... etc etc

Multiply any given number by two and you have the next number in the series.

So where do the 0s & 1s fit in? First it should be noted that in the answer above, a "switch" does not mean a physical switch. It is a CONDITION. Once the condition is met the "switch" is on. In the code above, each number is its own "switch" (condition). The state of the switch is determined by a 0 or 1. (Odlyzko, 81-93)

So lets say you want to define the number 43710 in binary code. The code would be as follows:

0101010101010101.

Why? Because in the number 43710 there is: one 32784, one 8196, one 2048, one 512, one 128, one 32, one 8 and one 2 (add these numbers to each other and you have 43710). The length of a line of binary code is determined by the number that it produces (longer numbers mean longer lines of code). Binary code is not written by humans, it is written by machines. It has no usefull function to us as humans other than to simplify the definition of inordinatly large numbers. (Odlyzko, 81-93)

The reference in the original answer to binary being a "computer" language, while true, lacks the specific definition of what exactly a computer is. A computer is more than something you buy from PC world, then take home and play games on. The term can be used to describe any machine that has the ability to transform languages (including the language of mathematics) into code (abbreviated) form. Early computers were nothing more than big rooms full of gears, cams and con-rods, and all they did was crunch numbers. They were big calculators, and in essence, that is all a modern computer is, albeit a fancy calculator!

In other words Let's start with what a binary number looks like:

01001010

“What the heck does this mean, and how do I represent this in more familiar decimal format” you ask. First, you have to know that each digit of a binary number is based on 2 to the power of x (as opposed to the decimal system that is based on the number 10). Here is a quick and easy chart you should study before continuing:

2 to the power of 0 = 1 (2^0)

2 to the power of 1 = 2 (2^1)

2 to the power of 2 = 4 (2^2) or (2*2)

2 to the power of 3 = 8 (2^3) or (2*2*2)

2 to the power of 4 = 16 (2^4) or (etc.)

2 to the power of 5 = 32 (2^5)

2 to the power of 6 = 64 (2^6)

2 to ...