Divide binary numbers - how it works

When programming or evaluating data, there is often the obstacle of having to divide binary numbers. However, this process is not too complicated. We'll tell you how it's done.

Division in the dual system: How to divide binary numbers

• The division in the dual system is very similar to that of the decimal system. The dividend is usually divided by the divisor here. This results in the quotient, sometimes with the remainder or decimal numbers. This is completely eliminated when calculating with binary numbers.
• Write to the division and follow the next steps. (In the next paragraph, the process is explained again using a practical example)
• Start by getting the number of the first digit of the dividend (number on the left) and compare it with the divisor (number on the right). If the number of divisors is the same or greater, a 1 is written in the first position of the quotient. If it is less than 0.
• Subtract the divisor from the dividend in the sequence if it is equal or greater. Otherwise, write the whole number on the next line. Subtract the next digit from the specified dividend and repeat these steps until you have reached the last digit. If there are any residual values ​​left, simply delete them. These are irrelevant.

Divide binary numbers - example

• In this example, the binary number of 15 (1111) is divided by the binary number of 5 (0101). The solution to this division should be 3 (0011).
• a) The first digit is written down and compared with the divisor 101. 1 is less than 101. Therefore 0 is written into the quotient.
• b) The 1 from the first line is adopted and the number of the next digit is written down. Again the comparison: 11 less than 101. So a second 0 comes in the quotient.
• c) The same process of transferring is repeated. Now we have the value 111, which is larger than the divisor 101. Consequently, a 1 is written in the quotient.
• d) A 1 in the quotient also means that in the number sequence the divisor 101 is subtracted from the number in line c) 111. This results in 10. Now the next digit is written down again and we get the value 101.
• This can be divided exactly by the divisor. This results in a 1 in the quotient and the residual value is 0.

It is often helpful to convert binary numbers to decimal numbers. On the next page you will find the perfect instructions for this.