Convert Decimal to Octal

A number system is called a positional number system due to the value of each symbol (i.e. digits and alphabets) in a number depending on the position within a number.

Numbers can also be the fractional part similar to the decimal used by us. The symbol in the rightmost position of the integer part is given as the number zero.

There are different types of number systems like decimal numbers, binary numbers, octal numbers, hexadecimal numbers, etc.

Decimal Numbers:

• Decimal number system is used in our day-to-day life.
• It is known as the base-10 number system since 10 digits from 0 to 9 are used.
• A number that is presented by its two values i.e. – symbol values (any digits 0 to 9) and positional value (in terms of base value).
• For example the below figure shows the integer and fractional part of the decimal number 237.25 along with the computation of the decimal values with the help of positional value

Binary Numbers:

The ICs (Integrated Circuits) in a computer are made up of a large number of transistors which are activated with the help of electrical signals (low/high) they receive. The ON / high and OFF / low are the two states of transistors that are represented as 0 and 1 respectively.

These two digits zero and one form the binary number system. It is also referred to as a base-2 system as it has only two digits.

It can be mapped as an equivalent decimal number which can be easily understood by humans. For example, the binary numbers are 1001011, 1011, 101, 111111.01, etc. Binary values of the digits one to nine of a decimal number system are as follows:

Octal Numbers:

• With the increase of values of the decimal numbers, the values of the bits (0 and 1) in binary representation also increase.
• Sometimes binary numbers are so large that it becomes difficult to manage.
• Octal numbers are devised for the compact representation of binary numbers. 
• Octal number system is called a base-8 system as it has a total of 8 digits from 0 to 7 and positional values are expressed in the power of 8.
• Three binary digits are sufficient to represent any octal digits.
• For example, octal numbers are as follows i.e. (237.05)8, (13)8, (617.24)8.

Conversion from Decimal to other Number Systems-

To convert decimal numbers to another number system like binary, octal, hexadecimal, etc. following steps are used.

Step 1: divide the given number according to the base value of the number system which needs to be converted.

Step 2: note the remainder.

Step 3: keep on dividing the quotient with the base value and note down the remainder until the quotient is zero.

Step 4: write the noted remainders in reverse order (i.e. from top to bottom).

Decimal to Binary Conversion:

• Since the base value of the binary number system is two then the decimal value is repeatedly divided by two by following the above steps until we get the quotient as zero.
• Record the remainder after each division and write the remainders in the reverse order in which they are computed.

Decimal to Octal Conversion:

• As we know the base value of the octal number is eight, so the decimal number is repeatedly divided by 8 to get the equivalent octal number

Conversion of Decimal to other Number System in Excel:

To convert the decimal numbers to another number system like binary, octal, hexadecimal, etc. in excel following steps are used

• Simple formulas are used to convert decimal to another number system in excel.
• First select the blank cell in the excel sheet, and type the Formula = DEC2BIN (A1) to convert decimal to binary number.
• Press enter to get the result of the given decimal number.
• If you want more results then drag the auto-fill down or right to fill the other cells.
• In the same way we can convert the decimal number to an octal number using the following formula.
• Formula used to convert decimal to octal in excel is Formula = DEC2OCT (A1).
• From the above-given formula “A1” is the cell that is given to convert.

Conversion of Decimal to Octal Examples:

Example 1:

Convert (122)10 to an octal number.

Solution:

• To convert decimal to octal divide 122 / 8 we get quotient as 15 and remainder as 2.
• Again divide 15 / 8 we get the quotient as 1 and the remainder as 7
• Again divide 1 / 8 we get the quotient as zero and remain as one.
• Therefore, (122)10 = (172)8.

Example 2:

Convert decimal number (100)10 to the octal number system.

Solution:

To convert decimal to octal following steps are used

• Firstly, we have divided the decimal value 100 by 8; here we get the quotient as 12 and remainder as 4.
• To get more remainders again divide 12 by 8; then we get quotient as 1 and remainder as 4.
• Lastly we divide decimal number 1 by 8; here we get quotient as zero and remainder as 1.
• Therefore, the result of (100)10 = (144)8.

Example 3:

Convert decimal number (321)10 to octal.

Solution:

The following steps are used to convert decimal to octal.

• Divide the given decimal number 321 by 8, after dividing we get the quotient as 40 and the remainder as 1.
• Again divide decimal number 40 by 8; here we get quotient as 5 and remainder as zero.
• Therefore, (321)10= (501)8.

Conclusion:

From the above content, we learned, what is a number system, what different types of numbers and their definitions? How to convert the decimal number to other number systems and a few examples.