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Converting Hexadecimal to Octal numbers

May 28 • General • 8912 Views • 4 Comments on Converting Hexadecimal to Octal numbers

                             CONVERSION FROM HEXADECIMAL TO OCTAL

Hexadecimal number are converted to its equivalent octal by converting the hex to equivalent binary and then octal respectively. Here we will be discussing CONVERSION FROM HEXADECIMAL TO OCTAL NUMBER in details

CONVERSION FROM HEXA TO  OCTAL Occurs in two steps:

1.HEXA TO BINARY CONVERSION

In this method,each digits of the  hexadecimal number is replaced  by its  4   bits equivalent,first we find the binary equivalent of the digit.If,it is  not in 3 bits ,then the zeroes are placed before the binary equivalent to make  it 4 bits using the following table::

HEXADECIMALBINARY
00000
10001
20010
30011
40100
50101
60110
70111
81000
91001
A1010
B1011
C1100
D1101
E1110
F1111

example

Convert (524.36)16  into its binary equivalent?

First of all,convert each of the digits into its binary bits  and then group the subsequent bits into 4 bits .If,they all are not  able form the group of 4 then, zeroe’s(0) are left padded to form the 4 bit pair.

5              2                  4           .               3              6

0101       0010              0100                  0011               0110     ( 4 bits  representation )

(524.36)16       =    (0101  0010  0100 .  0011  0110)2

 2.BINARY TO OCTAL  CONVERSION

After finding the binary equivalent of the hex number,the bits are grouped into groups of 3 bits starting at the     LSB .Then each digits are converted into its octal equivalent using the following table:

BINARYOCTAL
0000
0011
0102
0113
1004
1015
1106
1117

Example:

convert the  binary number 11011.1011 to its octal equivalent

This conversion is simple.In this case ,first the binary bits are grouped  into 3 bits .If ,they are not forming  then zeroe’s are left  padded .After that each groups are converted into its octal equivalent using the table:

11011.1011

011    011   .  101    100

3        3           5           4

(11011.1011)16      =           (33.54)8

QUESTION AD ANSWERS

Q.Convert  (7FD6)16     into its octal equivalent?

Ans:   First the individual digits are converted into its binary bits(each having 4 bits)

           7                    F                       D                      6

         0111              1111                  1101                 0110    (representing in 4 bits )

After that the subsequents bits are grouped into 3 bits.If.they are unable to form group of 3 the zero padding is done from the left.

    111              111            111                   01 0            110  (taking 3 bits together)

After that simply we  convert the binary bite to its equivalent octal number.

  7                 7                    7                       2                  6 ( octal equivalent)

(7FD6)16     =(77726)8      

Q.Convert  (ABCD)16     into its octal equivalent?

Ans: First the individual digits are converted into its binary bits(each having 4 bits)

    A                  B                         C                    D

  1010              1011                  1100                 1101      (representing in 4 bits)

After that the subsequents bits are grouped into 3 bits.If.they are unable to form group of 3 the zero padding is done from the left.

   001      010           101           111            001           101   (pairing 3 binary bits together)

After that simply we convert the binary bite to its equivalent octal number.

  1             2                5             7                 1             5     (octal equivalent)

So, (ABCD)16   =(125715)8       

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