Binary Octal and Octal Binary Conversions

           An octal number can be converted into its binary equivalent by replacing each octal digit with its
three-bit binary equivalent. We take the three-bit equivalent because the base of the octal number
system is 8 and it is the third power of the base of the binary number system, i.e. 2. All we have then
to remember is the three-bit binary equivalents of the basic digits of the octal number system. A binary
number can be converted into an equivalent octal number by splitting the integer and fractional parts
into groups of three bits, starting from the binary point on both sides. The 0s can be added to complete
the outside groups if needed.
 
Example 1.6
Let us find the binary equivalent of (374.26)8 and the octal equivalent of (1110100.0100111)2
Solution
• The given octal number = (374.26)8
• The binary equivalent = (011 111 100.010 110)2
= (011111100.010110)2
• Any 0s on the extreme left of the integer part and extreme right of the fractional part of the equivalent
binary number should be omitted. Therefore, (011111100.010110)2
= (11111100.01011)2
• The given binary number = (1110100.0100111)2
• (1110100.0100111)2
= (1 110 100.010 011 1)2
= (001 110 100.010 011 100)2
= (164.234)8