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All computers use a binary number system, that relies upon just two symbols, typically 0 and 1. In this lesson, you’ll learn about the advantages of using the binary number system, as well as some of its practical applications.

What Is the Binary System?

There is a bumper sticker out there that reads:’There are 10 kinds of people, those who understand binary and those who don’t.’If you don’t already understand why this is funny, you will by the end of this lesson.The most commonly used number system, called base-ten, uses ten digits: 0-9.

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By comparison, the binary number system, or base-two, is a counting technique that uses two digits: 0 and 1. Here, the prefix ‘bi’ means ‘two.’In this system, each place value is a power of two, where the first place to the left of the decimal point is 2^0, the second place is 2^1 and so on. Each number is called a bit and is pronounced separately. For example, when referring to this binary number:1011We’d say ‘one zero one one.’

Applications

The most common application for the binary number system can be found in computer technology.

All computer language and programming is based on the 2-digit number system used in digital encoding. Digital encoding is the process of taking data and representing it with discreet bits of information. These discreet bits consist of the 0s and 1s of the binary system.For example, the images you see on your computer screen have been encoded with a binary line for each pixel. If a screen is using a 16-bit code, then each pixel has been told what color to display based on which bits are 0s and which bits are 1s. As a result, 2^16 represents 65,536 different colors!We also find the binary number system in a branch of mathematics known as Boolean algebra. This field of mathematics is concerned with logic and truth values.

Here, statements that are either true or false are then assigned a 0 or 1.

Advantages

The biggest advantage of the binary number system is its simplicity. Any device with an on/off switch can be converted into a computing devise using the binary number system, with 0 representing ‘off,’ and 1 representing ‘on.

‘ As the switches used in computer language are either on or off, they can be easily read with little possibility of error.In computations, the binary number system is simpler to use than the base-ten or decimal system with fewer computations. For instance, there are only three computations used in addition:

  1. 0 + 0 = 0
  2. 0 + 1 = 1
  3. 1+1 = 10

Multiplication in the binary number system also involves the use of three computations:

  1. 0 x 0 = 0
  2. 0 x 1 = 0
  3. 1 x 1 = 1

By contrast, the base-ten or decimal system requires knowledge of 100 computations.

Lesson Summary

While the most commonly used number system is base-ten, the binary number system is also important. It is a counting system with only two digits.

These digits are typically 0 and 1. Each place value is a power of 2.Computer language uses a binary number system with zero representing an ‘off’ position and one representing an ‘on’ position. Advantages include ease of use in coding, fewer computations and less computational errors.

The binary number system can also be used in Boolean algebra.Now that you’ve finished this lesson, take a look at that bumper sticker:’There are 10 kinds of people, those who understand binary and those who don’t.’The ’10’ is a binary number, which really means 2.

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