Understanding the basics of digital mathematics is the foundation of all electronics and technology. Every child starts by learning base-10, radix or the decimal system. This system uses the number 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system uses a place value holder. When you examine the number 453. When you consider that number 3 that represents 3 while the 5 represents the value of 5 tens or 50. The 4 then obviously represents 4 hundred or 400. If we then add the values 400 + 50 + 3 = 453. The base-10 system means that 10 digits are used in each placeholder. Digital systems use the same methods to add, subtract and other functions using not a base-10, but a base-2 system which uses 2 digits in each placeholder spot.
Okay, so how is this whole thing important and why base-2? Let’s step back and consider the fundamentals of a digital system. All digital systems are based on electricity running over a wire. Now let’s add two more pieces a switch and a light. When I flip the switch to a closed state electricity flows through the wire to turn the light on. When I break the circuit or open the switch the light turns off. All of the base 2 come from this basic principle of turning a light on or off. In digital and especially computer systems this is done very rapidly to simulate millions of light switches being turned on and off over and over again. In digital systems, the light off represents a 0 and the light turned on represents a 1. We can’t have the light halfway on or halfway off from how we see it, the light is either on or off. This is where the 0 and the 1 come from while we can’t have a 2 because the light can only exist in two states. This is why the base-2 system is so important. The word digital means: resembling a digit or finger. I like to think that digital is the finger that is flipping on and off a light switch. So we know that digital systems use two numbers (0,1). In the base-10 system we call place holder’s digits in the base-2 system we call placeholders a bit. The word bit is actually a contraction of binary digit.
I am not going to get in the mathematics of things today but talk more about naming conventions used by digital systems and is most visible when used for computer systems. If you have ever worked with the metric system (kilometer, kilograms, centimeters) versus the Imperial system (miles, lbs, inches) you know that there is a different way of counting using the units.
Just like converting from kilometers to miles, there is a way to shift between base-2 and base-10 systems. Just like all other mathematical practices, there is a way to convert between these systems. Tomorrow let's learn the conversion and get into how to think in binary.
Comments, thoughts, and even dislikes are always welcome I love to get feedback. It helps me grow on steem. This content came from my blog Principles of Tech
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