Number Systems in Real Life Situations

A number system is of great significance in our daily lives and even more than that in the subject of Mathematics. This system represents the specific identity that a number possesses on the number line and provides it with a significant notation. It also represents the arithmetic structure of the number. It helps us in calculating the numbers using which we can get a specific number. The number system has different types of systems using which you can represent a number in more than one way. 

Examples of the number system

The entities that we use to count the objects are the result of the same number system that we are trying to learn. These help us keep a check on the physical quantities. And, the use of these is not limited only to Physics or Mathematics, these are beneficial in the computer programming languages as well. 

The examples of the conversions in the number system are given as follows:

Binary to Decimal 1101001

=> (1×2⁰) + (0×2¹) + (0×2²) + (1×2³) + (0×2⁴) + (1×2⁵) + (1×2⁶)

=> 1 + 0 +0 + 8 + 0 32 + 64

=> 105

=> (105)₁₀

Binary to Octal 1100011

Dividing this number into bits of three digits, the results of these three bits will be given as 3, 4 and 1 from the end to the beginning. Representing this in the form of the octal number system.

=> (143)₈

Binary to Hexadecimal 101010001

Similar to conversion into an octal number system, dividing this number into bits of four digits. The results that we will get out of these bits will be given as 1, 5 and 1 from the end to the beginning. To represent this binary number in the hexadecimal form, it will be written in the following way:

=> (151)₁₆

How is the number system used in real life?

The number system helps us in identifying the extent to which we need to limit an entity. These give us a general insight into the mathematical operations regarding the given numbers. This helps in the calculation of numbers using mathematical operations. This gives us a measure of the distance or quantity of an object. 

These play a significant role in helping us deal with currency. These help us in getting to the solutions of arithmetic progressions and equations. These are helpful for us in making general calculations and getting to a certain result. These help us keep up with general mathematics in daily life. 

Properties of the number system

The four main properties that are held by the numbers in the number system are as follows:

Commutative Property

This property signifies that if the position of numbers around a mathematical operation is swapped the result of that operation will still be the same. This property is held by the mathematical operation of addition and multiplication. However, the same can not be said in the case of subtraction and division. 

Associative Property

This property states that the result of the operation to a set of more than two numbers will stay the same regardless of the set of numbers on which the operation is applied for the first part. This property is applicable only for the mathematical operations that involve the addition and multiplication of numbers. 

Distributive Property

This property of the number system helps us in getting to a conclusion by expanding the expression that we are provided with. This property is applicable in the case of addition and subtraction of numbers. However, the secondary mathematical operation that is to be applied to the set of numbers needs to be multiplication. In this property, we split the numbers by expanding the given expression.

Identity Property

The identity property for the number system signifies that for a certain set of numbers related to the given mathematical operations, the identity of the given number will stay the same. In case of addition and subtraction, the identity property will signify the number 0. However, in the case of multiplication and division, the number will be 1.

Conclusion

There are four types of systems that come under the number system. These systems present different identities for a single number, but the meaning of the number in each case will remain the same. The numbers that are associated with a specific number system use a certain set of rules to be converted from one system to the other. However, all these systems follow the basic properties of the number system. These properties are commutativity, associativity, distributive and identity properties.