The number system we most familiar is Decimal (Base 10) which is used in our real world for counting numbers, cash, amount and other things. As a computer, it uses Binary (Base 2) number system, as they symbolizes for operating two states - on and off and its binary combinations. In computing, we also use Hexadecimal (Base 16) or Octal (Base 8) number systems, as a compact form of binary number representation.

Decimal Number system ranges from 0 to 9, which will count up next to 10 (ten). The lowest place is the rightmost position, and each successive position to the left has a higher place value. The rightmost position represents the "ones" column, the next position represents the "tens" column, the next position represents "hundreds", etc. Therefore, the number "123" represents 1 hundred(10²), 2 tens(10¹) and 3 tens(10⁰). Basically, after we count up the number from 0 to 9 (9 ones of 10⁰), there is no number count up next to 9. So, it will go up 1 at the left one position and the right position will go to start 0. The next number we count will be 10 which defines 1 tens of 10¹ and 0 ones of 10⁰.

Binary, Octal and Hexadecimal numbers goes the same way to count. When decimal number is based on 10, binary number will be based on 2, octal will be 8 and Hexadecimal will be 16.

So, the number of three digits position as follows. 

- 2² , 2¹ , 2⁰

- 8² , 8¹ , 8⁰

- 16² , 16¹ , 16⁰

So, we are going to learn to convert between those number systems (decimal, binary, octal and hexadecimal numbers).
Let's divided into three groups.
(1) Decimal ⇔ Binary, Octal and Hexadecimal numbers
(2) Binary, Octal and Hexadecimal ⇔ Decimal numbers
(3) Binary ⇔ Octal ⇔ Hexadecimal

(1) Decimal ⇔ Binary, Octal and Hexadecimal numbers

Let's see the example. 

Decimal Number : (23)₁₀

➡ (23)₁₀ To Binary Number (Base 2) => The result is (10111)₂ 

Note: The last digit will be the 1st remainder and it will go the sequence as 5th, 4th, 3rd, 2nd and 1st. 

➡ (23)₁₀ To Octal Number (Base 8) => The result is (27)₈ 

Note: The last digit will be the 1st remainder and it will go the sequence as 2nd and 1st. 

➡ (23)₁₀ To Hexadecimal Number (Base 16) => The result is (17)₁₆ 

Note: The last digit will be the 1st remainder and it will go the sequence as 2nd and 1st. 

(2) Binary, Octal and Hexadecimal ⇔ Decimal numbers

(111011)₂ To Decimal Number (Base 10) => The result will be (59)₁₀ 

(124)₈ To Decimal Number (Base 10) => The result will be (84)₁₀ 

(A2)₁₆ To Decimal Number (Base 10) => The result will be (162)₁₀ 

(3) Binary ⇔ Octal ⇔ Hexadecimal

During conversion among binary, octal and hexadecimal numbers, we have to convert to Base 2 Binary number format. We can represent three digits separator for Octal number and four digits separator for Hexadecimal number.