**Number System: Basic Concept**

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The number system, often known as the numeral system, is a way of designating or expressing numbers. It is employed to measure, compute, and count items.

**What does “number system” mean in mathematics? What Classifies the Number System (Number System Classification)?**

It is a way of consistently using digits or other symbols to numerically describe numbers. Each number is represented in a unique way. It also makes it possible for us to do mathematical operations like addition, subtraction, and division. **Number systems come in a variety of forms, but there are four primary categories:**

**Decimal Number System (Base 10):** This system generates numbers using 10 digits (0–9), each of which is placed in a specified location and has a place value that is the sum of several powers of 10.

For instance, in a base-10 system, the number 123.21 indicates the sum of (1 x 10^{2}) + (2 x 10^{1}) + (3 x 10^{0}) + (2 x 10^{-1}) + (1 x 10^{-2}).

**Binary Number System (Base 2):** Binary no. system only employs the digits 0 and 1 to represent numbers, and each digit is located at a specified location with a place value that is a sum of various powers of 2. An illustration of a binary number is 1110.

**Octal Number System (Base 8):** It creates numbers using eight digits (0–7), each of which is placed in a specified location and has a place value that is a sum of various powers of 8. For example, 315^{8} = 3 × 8^{2} + 1 × 8^{1} + 5 × 8^{0}

**Hexadecimal Number System (Base 16):** This system generates numbers using 16 digits (0–9 and A–F), each of which is placed in a specified location and has a place value that is a sum of multiple powers of 16.

**Hexadecimal Number System indicated in the table below:**

**Describe a number**

A number is a numerical value that may be used to count, identify, or measure items. In our daily lives, numbers play a significant part in everything from counting money and measuring the quantity of an object to identifying homes, bank accounts, automobiles, buses, trains, and airplanes. There are several types of numbers, including whole numbers, rational and irrational numbers, among others. Arithmetic is the study of computations involving numbers.

**Numerals**, sometimes known as number words or symbols, can be used to express it in language. A numeral system is an orderly approach to express any number using ten basic numeric symbols, or “digits,” in combination. **The Hindu-Arabic numeral system**, which enables the depiction of any number using a combination of 10 digits (0–9), is the most widely used system of numbers.

**Classification Of Numbers:**

**Real Number (R)**

All positives, all negatives, and zero are measured using Real Number. Examples of real numbers are -5, -4, 0, 2.5, 4, 2, etc. On the number line, a real number is one that appears. A new real number, which may also be expressed as a decimal, will arise from adding, subtracting, multiplying, or dividing all of the real numbers in the set. In this case, 4 plus 3 equals 7 (or 7.0).

The term “**Real ****number**” refers to any number that may be found on a number line. It is represented by R.

This definition states that a real number is one that can either be positive or negative and has decimal places after the point. As an example, 3, 4, 3.55 are real numbers. Thus, real numbers are measurable and may be manipulated.

**Imaginary Number**

If the squared value of a number is negative, it is said to be imaginary. Or, **number which is not real, is called imaginary number. ****It is denoted by symbol “i”.** Also, an imaginary number is the square root of a negative number.

i = square root of -1

or, i^2 = -1

**Can we show imaginary number on the number line?**

Number which cannot be quantified on a number line is called imaginary number.

**To put it another way,**

We represent imaginary number by drawing a vertical imaginary number line through zero. These two number lines together makes the complex plane. The number 0 is both real and imaginary.

**Complex number** includes both real numbers, imaginary numbers and sums and differences of them.

**What is the full name of the Base 1 Number System?**

The base-1 system, often known as the **unary numeral system**, is the simplest way to represent natural numbers. It is the simplest numeral system for representing natural numbers, with a sign for 1 being repeated N times to indicate a number N.

The empty string, or lack of a symbol, stands in for the number 0 (zero) in the unary system. Although the value of a digit does not rely on its position, the unary numeral system differs from all other bases in that it is a bijective numeral system.

In light of this, it is debatable whether it would be accurate to state that it has a base (or “radix”) of 1.

**What is Number Line? How does Number Line work?**

In mathematics, a number line is a straight line with numerals arranged in equal segments or intervals throughout its length. Infinite expansions are possible for numbers.