This document discusses converting between octal, binary, and hexadecimal number systems. It provides an example of converting the octal number 56 to its binary and hexadecimal equivalents. The octal number 56 is first converted to its binary representation 101110 by expressing each octal digit as 3 binary bits. Then, the binary number is converted to hexadecimal by grouping it into chunks of 4 bits and finding the corresponding hexadecimal digit, resulting in the hexadecimal equivalent of 2e.

1. Conversion of Octal
Number into Binary and
Hexa Decimal Numbers

2. Octal Numbers
A number system which has its base as 'eight' is called
an Octal number system. It uses numbers from 0 to 7. Let
us take an example, to understand the concept. As we
said, any number with base 8 is an octal number like
248, 1098, 558, etc.

4. Hexa Decimal Numbers
Hexadecimal is the name of the numbering system
that is base 16. This system, therefore, has numerals 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15. That means that
two-digit decimal numbers 10, 11, 12, 13, 14, and 15 must
be represented by a single numeral to exist in this
numbering system.

6. Binary Number
Binary number is defined as a number that is
expressed in the binary system or base 2
numeral system. It describes numeric values by
two separate symbols; 1 (one) and 0 (zero).

7. Example-1 Convert octal number 540 into binary number.
According to above algorithm, equivalent binary number
will be,
= (540)8
= (101 100 000)2
= (101100000)2
Convert octal number into binary
number.

8. Conversion of Octal Numbers into
Hexa Decimal Numbers
Octal Binary Hexadecimal
Let's convert (56)8 into hexadecimal
Step 1 : Convert (56)8 into Binary
In order to convert the octal number into binary, we need to express every
octal value using 3 binary bits.
Binary equivalent of 5 is (101)2.
Binary equivalent of 6 is (110)2.
= (56)8
= (101)(110)
= (101110)2

9. Step 2 : Convert (101110)2 into Hexadecimal
In order to convert the binary number into hexadecimal, we need
to group every 4 binary bits and calculate the value[From left to
right].
(101110)2 in hexadecimal
= (101110)2
= (10)(1110)
= (2)(14)
= (2e)16
This method is relatively easy compared to the below method.
14 quivalent hexadecimal is e.