Hex–Octal and Octal–Hex Conversions

       For hexadecimal–octal conversion, the given hex number is firstly converted into its binary equivalent
which is further converted into its octal equivalent. An alternative approach is firstly to convert the
given hexadecimal number into its decimal equivalent and then convert the decimal number into an
equivalent octal number. The former method is definitely more convenient and straightforward. For
octal–hexadecimal conversion, the octal number may first be converted into an equivalent binary
number and then the binary number transformed into its hex equivalent. The other option is firstly to
convert the given octal number into its decimal equivalent and then convert the decimal number into
its hex equivalent. The former approach is definitely the preferred one. Two types of conversion are
illustrated in the following example.
 
Example 1.8
Let us find the octal equivalent of (2F.C4)16 and the hex equivalent of (762.013)8
Number Systems 11
Solution
• The given hex number = (2F.C4)16.
• The binary equivalent = (0010 1111.1100 0100)2
= (00101111.11000100)2
= (101111.110001)2
= (101 111.110 001)2
= (57.61)8.
• The given octal number = (762.013)8.
• The octal number = (762.013)8
= (111 110 010.000 001 011)2
= (111110010.000001011)2
= (0001 1111 0010.0000 0101 1000)2
= (1F2.058)16.