**Important points of the number system**

The decimal number system has a base of 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands, and so on.

The base 2 number system is also known as the binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number.

In the octal number system, the base is 8 and it uses numbers from 0 to 7 to represent numbers. Octal numbers are commonly used in computer applications.

In the hexadecimal system, numbers are written or represented with base 16. In the hex system, the numbers are first represented just like in the decimal system, i.e. from 0 to 9 and A to F.

**Number system Example**

**1.**** ****Convert (1001001100)**_{2} to a decimal number**.**

= 1 × 2^{9} + 0 × 2^{8} + 0 × 2^{7} + 1 × 2^{6} + 0 × 2^{5} + 0 × 2^{4} + 1 × 2^{3} + 1 × 2^{2} + 0 × 2^{1} + 0 × 2^{0}

= 512 + 64 + 8 + 4

= (588)_{10}

**2.**** ****Convert hexadecimal 2C to decimal number.**

We need to convert 2C_{16} into binary numbers first.

2C → 00101100

Now convert 00101100_{2} into a decimal number.

101100 = 1 × 2^{5 }+ 0 × 2^{4} + 1 × 2^{3 }+ 1 × 2^{2} + 0 × 2^{1} + 0 × 2^{0}

= 32 + 8 + 4

= 44

Hey teachers, if you are looking for unit tests, activities, worksheets, quiz, practice test papers that are suitable for 6th grade math, here's the compilation of lessons suitable for 6th grade to share with your students.

Studying the number system is important as students learn about a unique representation of every number and represents the arithmetic and algebraic structure of the figures.