# Arithmetic operations in binary number system

Binary arithmetic operations are the set of operations that allow one to manipulate binary numbers. Binary operations are similar to those used for the decimal system, but the calculations are slightly different.

First, we need to understand the concept of binary numbers. A binary number is a sequence of digits that can only be 0 or 1. For example, 101100 is a six-digit binary number. Binary numbers are used to represent data and instructions in computer systems.

To perform any arithmetic operations on a binary number, we need to understand the concept of two’s complement. Two’s complement is a representation of a binary number in which the most significant bit is considered to be the sign bit. If the bit is 0, then the number is positive, and if the bit is 1, then the number is negative.

Arithmetic operations in the binary number system are similar to those in the decimal number system, but they are performed using only the digits 0 and 1. The four basic arithmetic operations are addition, subtraction, multiplication, and division.

The most common binary arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic operations in the binary number system are similar to those in the decimal number system, but they are performed using only the digits 0 and 1. The four basic arithmetic operations are addition, subtraction, multiplication, and division.

**Addition:**

In binary addition, we add two binary numbers by using the same process as we do in the decimal system. The only difference is that we only use 0s and 1s instead of 0 through 9. We start from the rightmost position and add the two digits, and if the sum is greater than 1, we carry over the remainder to the next position.

To add two binary numbers, start by adding the rightmost (least significant) digits, just as in decimal addition. If the sum is 0 or 1, write it down. If the sum is 2, write down 0 and carry 1 to the next column. If the sum is 3, write down 1 and carry 1 to the next column.

Repeat this process for each column, carrying any 1s to the next column as necessary.

**Example:**

```
1011 (binary)
+ 1101 (binary)
------
10100 (binary)
------
```

**Subtraction:**

Subtraction is similar to addition, except that instead of carrying the remainder we borrow it from the next position. In order to borrow, we need to subtract 1 from the number to the left of the position from which we need to borrow.

To subtract two binary numbers, start by subtracting the rightmost digit of the second number from the rightmost digit of the first number, just as in decimal subtraction. If the first number is smaller than the second number, borrow 1 from the next column to increase the first number. Then subtract the second digit from the first digit, and repeat this process for each column.

**Example:**

```
1011 (binary)
- 1101 (binary)
------
-0010 (binary)
------
```

**Multiplication:**

Multiplication is the same in binary as it is in the decimal system. We start from the rightmost position and multiply each digit by the other number. We add up all the products and put the result in the appropriate position.

To multiply two binary numbers, multiply the rightmost digit of the second number by each digit of the first number, starting from the rightmost digit, and write the results underneath. Then shift the second number one digit to the left and repeat the process, adding the results together as you go.

Example:

```
101 (binary)
* 110 (binary)
------
1010 (binary)
1010 (binary)
------
11110 (binary)
------
```

**Division:**

Division is similar to multiplication, except that the divisor is shifted to the left until it is equal to the dividend. We keep subtracting the divisor from the dividend until the dividend becomes zero. The number of subtractions tells us how many times the divisor goes into the dividend.

To divide one binary number by another, use long division as in decimal division. Divide the leftmost digit of the dividend by the leftmost digit of the divisor, and write the quotient underneath. Then multiply the divisor by the quotient, subtract the result from the dividend, and bring down the next digit. Repeat this process until the remainder is smaller than the divisor.

**Example:**

```
1010 (binary) ÷ 11 (binary)
------
1)1010
11
----
1
1 0
---
1
```

Therefore, the quotient is 10 (binary) and the remainder is 1 (binary).