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
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
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
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
Divide 111111 by 11
Divide 10001 by 10