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HOW TO CONVERT OCTAL TO BINARY,HEXADECIMAL TO BINARY? EXPLAIN WITH 5 EXAMPLE EACH?

OCTAL TO BINARY

The octal number system has a base of 8 i.e. the number of digits in the octal number system is eight(8) starting from 0 to 7.

The highest digit in the octal number system is (7)8, from the number system conversion table we can see that (111)2 is the binary equivalent of the highest octal digit and three binary digits(bits) are required to represent the highest octal digit.

In the octal to binary conversion method, we will convert each digit from the given octal number into three bit binary number starting from the right most octal digit(LSD) to the left most digit(MSD) and at the end combine each three bit binary number to form the binary equivalent of given octal number.

Let us take a number 348

Now the binary equivalent of 3 is 011 and that of 4 is 100.

So the desired binary equivalent of the octal number is 111002

HEXADECIMAL TO BINARY

Hexadecimal, is a number system of base 16

This number system is especially interesting because in our casually used decimal system we have only 10 digits to represent numbers. As hex system has 16 digits, the extra needed 6 digits are represented by the first 6 letters of English alphabet. Hence, hex digits are 0,1,2,3,4,5,6,7,8 and 9 A, B, C, D, E, F.

This below example is the basic principle used in this Hexadecimal to Binary conversion. To calculate the equivalent binary number for a given Hex number, each digit of a hex number is individually converted to its binary equivalent. For example the equivalent binary number for 3FDH can be written as 

3 = 0011; F = 1111; D = 1101

The Binary Number = 0011 1111 1101


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