Bases

A number base (also known as base) for short is a numeral system that tells us about the unique or different symbols and notations that can be used to represent a value.

For example, the base 2 number system tells that there are only 2 unique notations 0 and 1 to represent the value.

The most commonly used number base is base 10, also known as the decimal number system. The decimal number system uses ten different notations which are the digit 0-9 to represent a value Bases can be either positive, negative, 0, complex, or non-integer. The most frequently used bases are base 2 and base 16. They are also used for calculating and are known as binary, and hexadecimal respectively.

What is a Base Number?

A base number is a number raised to the power that represents the number of units of a number system. For example, the base number of the binary number system is 2.

For Example,

y^x

Here, y is a base number.

Base 2 Number System

In Mathematics, the base 2 number system, also known as the binary number system uses 2 as the base and therefore requires only two digits i.e. 0 and 1 to represent any value, rather than 10 different symbols required in the decimal number system. The numbers from 0 to 10 in the binary number system are represented as “.” .The base 2 number system is widely used in Mathematics and Computer Science as bits are easy to create using physically logic gates (the logic gates are either open or closed meaning 0 or 1).

Counting in Different Bases

Counting in different bases substitutes the base 10 with a different bases. We often use Base 10. It is our decimal number system. It has 10 digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

We count numbers with base 10 as shown below:

Let us Understand How to do Counting in Different Base

(Base 2) Binary Number System Has Only 2 Digits: 0 and 1

We count the base 2 like shown below:

(Base 3) Ternary Number System Has 3 Digits: 0,1, and 2

We count numbers with base 3 as shown below:

(Base 4) Quaternary Number System Has 4 Digits: 0, 1, 2, and 3

We count numbers with base 4 as shown below:

(Base 5) Quinary Number System Has 5 Digits: 0, 1, 2, 3, and 4

We count numbers with base 5 as shown below:

(Base 6) Senary Number System Has 6 Digits: 0, 1, 2, 3, 4, and 5

We count numbers with base 6 as shown below:

(Base 7) Septenary Number System Has 7 Digits: 0, 1, 2, 3, 4, 5, and 6

We count numbers with base 7 as shown below:

(Base 8) Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7

We count numbers with base 8 as shown below:

Nonary (Base 9) Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8

We count numbers with base 9 as shown below:

(Base 10) Decimal Number System Has 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 9, and 10

We count numbers with base 10 as shown below:

Facts to Remember

In the number system, base, also known as radix, is the number of different digits or combinations of digits and letters that the number system uses to represent numbers.