In this article, we will learn about octal arithmetic-octal addition and octal subtraction. Arithmetic involves the operations with numbers. This article describes how to perform basic arithmetic operations on octal numbers; hence, it is called octal arithmetic.

**What is an Octal Number System?**

In digital electronics, an octal number is a type of number system having a base of eight (8). This number system has 8 unique symbols to represent different numerals of the system. They are 0, 1, 2, 3, 4, 5, 6, and 7. Hence, any number consisting of only these 8 symbols can be referred to as an **octal number**.

An octal number is typically represented in the octal system as shown below.

For example, (542)_{8}, (1002)_{8}, and (377)_{8} are examples of** octal numbers.**

The most important thing that we have to remember while performing octal arithmetic operations is that if the result of the operation is greater than 7, there would be a carry.

Let us now learn about the addition and subtraction arithmetic operations of octal numbers, i.e., octal arithmetic.

**Octal Addition**

The arithmetic operation in which two octal numbers are added together to find their sum is termed the addition of octal numbers.

The addition of octal numbers is one of the most basic arithmetic operations.

Let us take an example to understand the octal addition-** base 8 addition**– of octal numbers.

**Example – Add (517) _{8} and (253)_{8}.**

**Solution** – The step-by-step method of **adding octal numbers** is given below.

**Step (1)** – Addition of rightmost digits, i.e., 7 and 3:

(7)_{8} + (3)_{8} = (12)_{8}

Here, 2 will be written as sum, and 1 is as carry.

**Step (2)** – Addition of next to digits, i.e., 1 and 5:

(1)_{8} + (1)_{8} + (5)_{8} = (7)_{8}

Here, the first (1)_{8} is a carry from the previous step. The sum result is 7.

**Step (3)** – Addition of leftmost digits, i.e., 5 and 2:

(5)_{8} + (2)_{8} = (7)_{8}

Here, the sum result is 7.

This addition is illustrated in the following figure.

Hence, this is all about the addition of octal numbers.

**Solved Examples- Addition of Octal Numbers**

**Q.1 (172) _{8} + (438) _{8}**

**Solution:**

**Therefore, sum = 632 _{8}**

**Q.2 (178) _{8} + (846) _{8}**

**Solution:**

**Therefore, sum = 1246 _{8}**

**Q.3 (642) _{8} + (148) _{8}**

**Solution:**

**Therefore, sum = 1012 _{8}**

**Q.4 (125.32) _{8} + (249.46) _{8}**

**Solution:**

**Therefore, sum = 377.17 _{8}**

Let us now learn to perform the subtraction of octal numbers.

**Octal ****Subtraction**

**Subtraction**

The subtraction of octal numbers is similar to that of the decimal numbers. The only difference is in borrow taken during operation. In the **octal system**, when we take a borrow, it will be considered 8.

Let us understand the subtraction of octal numbers with the help of an example.

**Example** – Subtract (125)_{8} from (564)_{8}.

**Solution** – The step-by-step process of subtracting the (125)_{8} from (564)_{8} is explained below.

**Step (1)** – Subtracting the rightmost digits, i.e., 5 from 4:

(4)_{8} – (5)_{8}

Since, here, 4 is less than 5. Therefore, we need to borrow from the next digit, i.e., 6.

(8)_{8} + (4)_{8} = (12)_{8}

Hence, after taking a borrow, the digit 4 is now become 12. Let us now subtract 5 from 12, i.e.,

(12)_{8} – (5)_{8} = (7)_{8}

Here, 7 is the rightmost digit of the difference.

**Step (2)** – Subtracting the next digits, i.e., 2 from 6:

As we know, we took a borrow from the digit 6 in the previous step; hence,

(6)_{8} – (1)_{8} = (5)_{8}

Thus, we left with 5 in place of 6. Hence, the subtraction will become,

(5)_{8} – (2)_{8} = (3)_{8}

Hence, the difference is 3.

**Step (3) –** Subtracting the leftmost digits, i.e., 1 from 5:

(5)_{8} – (1)_{8} = (4)_{8}

Here, the difference is 4.

The complete subtraction of the given octal numbers is shown in the following figure.

Hence, this is how we can easily perform subtraction of octal numbers.

**Solved Examples- Subtraction of Octal Numbers**

**Q.1 (430) _{8} – (305) _{8}**

**Solution:**

**Therefore, difference = 123 _{8}**

**Q.2 (742) _{8} – (563) _{8}**

**Solution:**

**Therefore, difference = 157 _{8}**

**Conclusion**

In this article, we discussed **how to add and subtract octal numbers**. Here, we have studied the step-by-step process of adding and subtracting the octal numbers with the help of examples.