Hexadecimal to Octal Conversion
To convert a Hexadecimal number to an Octal number we have to First convert the Hexadecimal number to a Decimal number and then the Decimal number to an Octal number.
Steps to Convert Hexadecimal Number to Decimal Number
We can use the following steps to convert hexadecimal numbers to decimal numbers.
Step 1: Write the corresponding decimal value for the given hexadecimal number.
Step 2: Multiply each digit of the obtained number with an increasing power of 16 starting from the rightmost digit.
Step 3: Sum all the products obtained in step 2.
Steps to Convert Decimal Number to Octal Number
We can use the following steps to convert decimal numbers to octal numbers.
Step 1: Divide the given decimal number by 8.
Step 2: Write down the quotient and remainder obtained.
Step 3: Divide the quotient obtained by 8.
Step 4: Repeat step 2 and step 3 until the quotient becomes 0.
Step 5: Write the obtained remainder in reverse order.
Let’s consider an example for better understanding.
Example: Convert 9B16 to an Octal Number.
Step 1: First convert 9B16 to decimal number:
Corresponding decimal value of 9 and B are 9 and 11 respectively.
9B16 = 9 × 161 + 11 × 160
9B16 = 9 × 16 + 11 × 19
B16 = 144 + 11 = 155
We get 9B16 = 15510
Step 2: Convert 15510 to Octal Number
155/8, Quotient = 19, Remainder = 319/8, Quotient = 2,
Remainder = 32/8, Quotient = 0, Remainder = 2
Writing the obtained remainders in reverse order we get:15510 = 2338
Hence we get 9B16 = 2338
What is Octal ?
Octal is a number system with a base of 8 i.e. it uses 8 numeric values, namely, {0, 1, 2, 3, 4, 5, 6, 7}. This number system is mostly used in the programming of computer programs. For example (32150.7642)8, (275)8, (324)8, (2243)8 are Octal numbers. In this article, we will discuss the octal number system.