Octal number can be converted into its binary equivalent by replacing each octal digit with its three bit binary binary equivalent.We take 3 bit equivalent because the base of the octal system is 8 and it is the third power of the base of the binary number system i.e 2. All we have to remember is the three bit binary equivalents of the basic digits of the octal system. A binary number can be converted into equivalent octal number by splitting the integer and fractional parts into groups of three bits ,starting from the binary point on both sides.
Example:
Example:
Let us find the binary equivalent of (374.26)8 and
the octal equivalent of (1110100.0100111)2.
Solution:
1)The given octal number = (324.26)8
2) The binary equivalent = (011 111 100.010 110)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
