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::
HEXADECIMAL | BINARY |
0 | 0000 |
1 | 0001 |
2 | 0010 |
3 | 0011 |
4 | 0100 |
5 | 0101 |
6 | 0110 |
7 | 0111 |
8 | 1000 |
9 | 1001 |
A | 1010 |
B | 1011 |
C | 1100 |
D | 1101 |
E | 1110 |
F | 1111 |
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:
BINARY | OCTAL |
000 | 0 |
001 | 1 |
010 | 2 |
011 | 3 |
100 | 4 |
101 | 5 |
110 | 6 |
111 | 7 |
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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