the Hexadecimal System

Conversion of Hexadecimal to…

Decimal:

The hexadecimal can be converted to decimal by using the 16ⁿ system…

Eg:

C6₁₆

Hexadecimal            C                   6

Decimal              ^* 12×16¹            6×16⁰      =    192   + 6    = 198₁₀  

                      *   (C is equal to 12 in the Number System Conversion of  hexadecimal)

Eg 2 :

FFD4.F₁₆

Hexadecimal            F               F                       D               4            .         F

Decimal               *15×16³     15×16²      **13×16¹      4×16⁰            .     15×16^-1

                            =61440 + 3840 + 208  + 4+0.9375

                            =65492.9375₁₀

(* 15 is equal to the  F in the Number System Conversion of hexadecimal…

  **13 is equal to the D in the Number System Conversion of hexadecimal…)

Binary:

The conversion of hexadecimal  to  binary  by 3 methods:

·         Converting to decimal and then to binary

·         According to the Number System Conversion between hexadecimal and binary

·         By using the 2ⁿ  system

Eg :

2C₁₆

Method 1: Converting to decimal and then to binary

Hexadecimal                2                     C                 

Decimal                  2×16¹               12×16⁰         =    32+ 12 =44₁₀

 

Then convert the decimal into binary by using division…

2	44
2	22          0
2	11          0
2	5          1
2	2          1
	1          0

                                                               

44₁₀ = 101100₂

And also can written as …

2C₁₆  =   101100₂

Method 2 : According to the Number System Conversion between hexadecimal and binary

Hexadecimal         2                 C

Binary               0010              1100

·         2C₁₆  =    10 1100₂

Method 3: By using the 2ⁿ system

---when  converting the binary into hexadecimal ,we need to group the binary into 4…and the 4 of grouped binary are indicated by the 2ⁿ system…

For example,   the most left of the  grouped binary indicate the 2³,next is 2² , followed by 2¹, and lastly is 2⁰

So,

2C₁₆ =  0010 1100₂

(0010₂ = ( 0×2³)+(0×2²)+(1×2¹)+(0×2⁰)=0+0+2+0=2₁₆;

1100₂  =(1×2³) + (1×2²) + (0×2¹) + (0×2⁰) = 8+4+0+0= 12=C₁₆)

Eg 2:

C6.F₁₆

We convert according the Number System Conversion between the hexadecimal and binary…

Hexadecimal                 C                     6               .                F

Binary                      1100                 0110                         1111

So,

C6.F₁₆ =  1100 0110.1111₂

Octal:

There are few ways to convert the hexadecimal to octal:

·         Convert the hexadecimal into decimal and then to octal

·         Convert the hexadecimal into binary and then to octal

Eg :

4A₁₆

Method 1: Convert the hexadecimal into decimal and then to octal

Hexadecimal          4                     A

Decimal               4×16¹            10×16⁰   =    64 + 10 =74₁₀

Convert to octal by dividing the decimal with 8…

8	74
8	9              2
	1              1

                                                                                            

4A₁₆  = 112₈

Method 2 : Convert the hexadecimal into binary and then to octal

Hexadecimal                    4                              A

Binary                       *   0100                      **1010

                           * ((0×2³) + (1×2²) + (0×2¹) + (0×2⁰) =4₁₆)

                         **((1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 10 =A₁₆)

4A₁₆ = 100 1010₂

Convert to octal by grouping the binary into 3…

100 1010₂  =  001 |  001 | 010₂

Then , according to the Number System Conversion between Octal and binary…

Octal	Binary
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

1001010₂ = 112₈

Or …

By using the 2ⁿ system…

100 1010₂ =     001    |     001    | 010₂

                    =((0×2²)+(0×2¹)+(1×2⁰)) |((0×2²)+(0×2¹)+(1×2⁰)) | ((0×2²)+(1×2¹)+(0×2⁰))

                    =1             |        1      |    2₈

Therefore ,

4A₁₆  =   112₈

Eg 2 :

6A.B₁₆

Converting to binary …

Hexadecimal            6                 A         .             B

Binary                   0110            1010     .          1011

6A.B₁₆ = 1101010.1011₂

Converting into octal…

1101010.1011₂ =   001 |101 |010. |101 | 100  

(According to the Number System Conversion between octal and binary)

                             =     1 |    5   | 2  .   |   5   |4₈

Therefore,

6A.B₁₆  =    152.54₈

by Chong Cai Ning B031210080 shinbachi123@hotmail.com