### What is a Binary Number System?

A binary number system represents the number with the base 2, it uses the digits 1 and 0. As it uses only two digits 0 and 1 and has a base of 2, it is called binary. The way we perform arithmetic operations on the decimal number system, similarly we can perform all arithmetic operations on binary numbers.Operations such as addition, subtraction, multiplication and division.

Binary division is an important part of binary arithmetic. Binary division is similar to that of decimal division operation. In this article we will study step by step methods to make binary division understand as much as possible. Long division is one of the easiest and most efficient ways to solve binary division.

### Binary Division Rules

Simplifying binary division is almost as easy as multiplying binary numbers, and involves our knowledge of binary multiplication. Just we have to take note of some rules while dividing two binary numbers. There are four rules associated with binary division. The binary division rules are as follows.

1÷1 = 1

1÷0 = 0

0÷1 = Meaningless

0÷0 = Meaningless

As binary numbers include only two digits i.e. 0 and 1, these four rules are all the possible conditions for the division of binary numbers.

Here is the stepwise procedure of how to divide two binary numbers.

### Four Steps to Binary Division

Likewise decimal division binary division also carries out four steps for division of numbers.

Division: First take the leftmost digit of the dividend, we attempt to divide it by the divisor which must be smaller than the dividend digits. This results in a quotient.

Multiplication: Once we have found the quotient we use it to multiply the divisor to obtain a product.

Subtraction: Having calculated the product in the previous step, we subtract that from the working dividend to calculate a remainder.

Bring Down : The final step is then to bring down the next digit in our original dividend, combine it with the remainder in the previous step and form a new working dividend. At this point, the process is repeated.

Let’s look some examples of applying this process for binary division,

### Binary Division Examples

Example: Divide 01111100 ÷ 0010

Solution:

Here the dividend is 01111100 and the divisor is 0010

The zero’s in the Most Significant Bit in both the dividend and divisor doesn’t change the value of the number. So remove the zero’s.

So the dividend becomes 1111100 and the divisor becomes 10.

Now, use the long division method.

10) 1 1 1 1 1 0 0 ( 1 1 1 1 1 0

- 1 0

____________

1 1

1 0

_________

1 1

-1 0

___________

1 1

-1 0

___________

1 1

-1 0

____________

0 0

0 0

_______________

0 0

Step 1: First, compare the first two numbers in the dividend with the divisor. Add the number 1 in the quotient place. Multiply, write it under the dividend and then subtract the value, you get 1 as remainder.

Step 2: Then bring down the next number from the dividend portion, now you have remainder and the value from dividend now do the step 1 process again

Step 3: Repeat the process until the remainder becomes zero.

Step 4: After you get the remainder value as 0, you have zero left in the dividend portion, so bring that zero to the quotient portion.

Therefore, the resultant value is quotient value which is equal to 111110

So, 01111100 ÷ 0010 = 111110

### Solved Example

Example 1: 101 Divide By 10

10) 1 0 1 ( 1

- 1 0

________

0 0 1

Example 2: Divide 11010 By 101

101 ) 1 1 0 1 0 ( 101

1 0 1________

0 0 1 1 0

- 1 0 1

_________

0 0 1

### Quiz Time

Divide 111111 by 11

Divide 10001 by 10

1. What is Binary Addition?

Binary addition is the addition of binary numbers. Binary addition islike addition in the decimal number system the difference is only of the base. Addition of binary numbers is carried out with the binary addition rules.

**Binary Addition Rules**

Addition of two binary numbers is as easy as the addition of a decimal number system. Just we have to understand some rules while adding two binary numbers. There are four rules associated with binary addition. The binary addition rules are as follows.

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 =10

2. How to Convert Binary Numbers to Decimal Number Systems?

Binary numbers are the number with base 2 and digits 0 and 1 while the decimal numbers are the numbers with digits 0 to 9 and base 10.

The formula for binary number to decimal number conversion is

For binary number with n digits:

d_{n-1} ... d_{3} d_{2} d_{1} d_{0}

The sum of the product of binary digits ( dn) and their power of 2 (2n) gives the decimal number.

decimal number = d_{0}×2^{0} + d_{1}×2^{1} + d_{2}×2^{2} + d_{3} x 2^{3}+ …...

**For Example**

Find the decimal value of 111001_{2}:

Binary number: 1 1 1 0 0 1

And their power of 2: 2^{5} 2^{4} 2^{3} 2^{2} 2^{1 }2^{0}

111001_{2}

= 1 x 2^{5} + 1 x 2^{4} + 1 x 2^{3} + 0 x 2^{2} + 0 x 2^{1} + 1 x 2^{0}

= 57_{10}