Warning: Math Intensive Discussion
The basic building blocks of electronic life are the digits zero and one. Depending on context, they may represent off and on or false and true, respectively. Without them, none of the digital devices on which we depend would function. Let me explain how binary is used to underpin our online world.
There are infinite number systems in the universe. In our contemporary life, we use the decimal system. Deci means 10 and decimal is a base-10 number system, meaning everything works in units of 10. Just think of the place values from elementary school math class: ones place, tens place, hundreds place, thousands place, and so on. Each of these places is an expression of ten to a power. The ones place is 100 which is 1. The tens place is 101 which is 10. And so on. There are a total of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Binary is a base-2 number system. Bi means 2 so we’re using units of 2 the same way we used units of 10 in decimal. The first place in all number systems is 1. That’s our starting place. The second place in binary is the twos place, just like in decimal it was the tens place. Each of these places is an expression of two to a power. The ones place is 20 which is 1. The twos place is 21 which is 2. And so on. There are a total of two digits: 0 and 1. In electrical systems, the 0 and 1 represent open and closed circuits or off and on switches.
Here is a simple example to illustrate how a binary number converts to a decimal value. This is the example from the picture, 112 = 310. The subscripts 2 and 10 indicate the base-two and base-ten number systems. This is how we know that we are looking at a binary number on the left of the equal sign and a decimal number on the right.
Now, we look at the place values. For our binary number we have 1 in the ones place and a 1 in the twos place. We have 1 set of 1 and 1 set of two or 1*1 + 2*1 which equals 3 in decimal.
Ta-Da! You are rocking binary numbers.
All numbers from any number system and all words in any language can be transformed into a series of binary numbers. If it takes two characters to represent the single decimal value of three, you can imagine that the number of binary digits necessary to represent even small words can quickly become unwieldy. For that reason, binary is used to represent data at the lowest levels of the network structure layer models. Binary is not used to represent data at network structure layers on which users directly interact.
Computer scientists, network engineers, and cryptologists, among others, have to convert between number systems including binary, decimal, and hexadecimal for many common tasks. In terms of cybersecurity, binary is used in many places. IP addressing uses binary. These are the Internet Protocol addresses that are issued to a device when it accesses the internet. Binary and other number systems are used in cryptography applications including encoding. We owe our digital world to the binary number system, so let’s hear it for these two modest little digits.
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