Number Base Conversion (Binary | Octal | Decimal | Hexadecimal) All in One

Number conversion is the process of converting one number base to another base. In computer science, we have to study about 4 types of number systems, binary, octal, decimal, and hexadecimal number. When we convert one number system to another number system, it will be a total of 12 different number conversion types, which are illustrated below. While converting one number base to another number base it will be better to use the following table.

1. Binary to Decimal
2. Octal to Decimal
3. Hexadecimal to Decimal 
4. Decimal to Binary
5. Octal to Binary
6. Hexadecimal to Binary
7. Binary to Octal
8. Decimal to Octal
9. Hexadecimal to Octal
10. Binary to Hexadecimal
11. Octal to Hexadecimal 
12. Decimal to Hexadecimal 

1) Binary to Decimal Conversion 

i) Convert 11100011101

Convert 1101011₂ = into equivalent decimal number

Method 1:

11010112
= 1×26+1×25+0×24+1×23+0×22+1×21+1×20 
= 64+32+0+8+0+2+1
= 10710

Method 2:

1101011₂

ii) Convert 111100110111₂ into an equivalent decimal number

Method 1:

1111001101112
= 1×211+1×210+1×29+1×28+0×27+0×26+1×25+1×24+0×23+1×22+1×21+1×20
= 2048+1024+512+265+0+0+32+16+0+4+2+1
= 3895

Method 2:

= 1×84+ 2×83+5×82+6×81+3×80
= 4096 + 1024 + 320 + 48 + 3
= 549110 

 = 7×164+10×163+2×162+11×161+13×160
 = 458,752 + 40,960+512+176+13
 = 50041310

5) Octal to Binary Conversion 

Convert 2763₈ into an equivalent binary number

Octal Number: 2763

3 group binary digits

:: 27638 = 010111110011₂

6) Hexadecimal to Binary

Convert AD710  into an equivalent binary number

       Hexadecimal Number AD7

       4 group binary digit 

:: AD7₁₀ = 101011010111₂

7) Binary to Octal Conversion

Convert 111000101102 into equivalent octal number

3 group binary digits  (Note: group the binary digits from right to left) 

:: 11100010110₂ = 346₈

8)  Decimal to Octal Conversion 

Convert 89652₁₀ into equivalent octal number

   :: 89652₁₀ = 257064₁₀

9) Hexadecimal to Octal Conversion

The process of converting a hexadecimal number into an octal number is that, at first, we convert a hexadecimal number into binary and after that, we convert the obtained binary number into an octal number.

Convert A9D5₁₆ into equivalent octal number

Step 1: Converting Hexadecimal number into a binary number

4 group binary digits

:: A9D516 = 10101001110101012
 Step 2: Now converting binary to octal number

   3 group binary digits
   001  010  100  111  010  101
    1    2    4    7    2    5

   So,  A9D516 = 1247258

10) Binary to Hexadecimal Conversion

Convert 10111010010001₂ into equivalent hexadecimal number

 4 group binary digits
 0010   1110   1001   0001
  2       E     9      1

   :: 101110100100012  =2E9116

11) Octal to Hexadecimal Conversion

The process to convert an octal number into hexadecimal first, we will convert an octal number into binary numbers system and after that again we convert the obtained binary number into hexadecimal number by making group of 4 binary digits.

E.g.    Convert 1247258 into hexadecimal number
Step 1: Converting octal to binary

:: 124725₈ = 001010100111010101₂

 Step 2: Now converting obtained binary number to octal
 Binary = 0010101001110101012

 Making 4 group binary digits from right  
 0000   1010   1001   1101   0101
  0       A     9       D     5

:: 0010101001110101012 = A9D516
So, 1247258 = A9D516

12) Decimal to Hexadecimal

Convert 9685₁₀ to equivalent hexadecimal number

:: 9685₁₀ = 25D5₁₆