What is Binary Division : Algorithm, Examples & Its Working

There are four types of arithmetic operations that can be performed on binary and decimal number systems addition (Add), subtraction (Sub), multiplication (Mul) & division(Div). A base-2 number system or binary number system is simply represented by the number with the base-2 and it uses two digits like ‘0’ & ‘1’. Here the arithmetic operations which are performed on binary numbers are similar to the arithmetic operations performed on decimal numbers. In computer programming languages, the binary number system is most frequently used which relies upon just two symbols, 0 and 1. So this article discusses an overview of binary division definition – working, rules with examples.


What is Binary Division?

In binary arithmetic operations, the binary division is a significant operation that uses binary digits like other types of binary operations. As compared to decimal system operation, binary division operation is similar apart from the base because this division uses base2 whereas decimal system uses base10. Generally, the binary division uses two binary numbers with base2 and that can be divided by using fundamental rules for this division.

What is the Formula of Binary Division?

For dividing 2-binary numbers, we just need to follow four some rule which is shown below. As compared to decimal division, the binary division is very simple when it follows the following rules. The following four rules of binary division are the achievable conditions for binary division.

Dividend Divisor

Result

1

1 1

1

1 Insignificant
0 1

0

0 0

Insignificant

Binary Division Algorithm

The step-by-step procedure of binary division is discussed below. The problems based on this division can be simply solved through the long division technique. This is one of the easiest & most efficient techniques for dividing binary numbers. In this division operation, the following algorithm steps need to follow.

Step-1

First, the divisor must be compared with the dividend. If the divisor is smaller than the dividend then we need to multiply it by 1 & the result becomes the subtrahend. After that, the subtrahend must be subtracted from the minuend to obtain the remainder. Similarly, if the divisor is higher than a dividend, then place zero as the quotient, and after that carry the 2nd bit of the dividend downward.

Step-2

After that take down the next bit from the dividend part & perform step 1 once more.

Step-3

Again a similar procedure needs to perform until the remainder turns into ‘0’ otherwise the complete dividend is divided.

Examples

The examples of binary division are explained below.

Example1:

Divide 1111100 with 10. In this example, 1111100 dividend & 10 is the divisor.

By using the long division technique, binary division can be done. The steps involved while performing this division are discussed below.

Step-1

Initially, the 1st two numbers need to compare within the dividend by the divisor. After that, add the ‘1’ number within the quotient position. Multiply and write it below the dividend and after that subtract the value, so you will get ‘1’ as the remainder.

Step-2

After that bring down the second number to the bottom from the portion of the dividend, so now you will have the remainder & the dividend value. Now perform again the step-1 method.

Step-3

Repeat the procedure again and again until the remainder turns to zero.

Step-4

Once you obtain the remainder value like zero, then you have ‘0’ left within the portion of the dividend, as a result, bring that ‘0’ to the portion of the quotient.

So, the value of the quotient is the resultant value and this value is equivalent to “111110”.

Thus, 1111100 (dividend) ÷ 10 (divisor) => 111110 (quotient value).

Binary Division Example1
Binary Division Example1

Example2:

Divide (1111000)2 by (100)2.

Example2
Example2

Binary Division Calculator with Steps

The binary division calculator simply explains how to divide two binary numbers and provides a step-by-step procedure to perform the division of the binary number. The steps involved in the division calculator are discussed below.

Select the Binary Representation

This setting simply describes the no. of bits your input divisor, dividend, & quotient can have.
Here, this dividend includes six significant bits.

Provide Input Numbers

The dividend is 101010.

The divisor is 110.

The calculator of binary division presents your quotient as well as the remainder within the binary & decimal system. So the binary numbers division results will be

Quotient: 111 (binary), 7(decimal)

Remainder: 0 (binary & decimal)

Binary Division Circuit Diagram

The two-bit binary division circuit diagram is shown below which can be designed with basic logic gates based on the binary division truth table.

Two Bit Binary Division Circuit
Two Bit Binary Division Circuit

The circuit diagram of binary division signifies a 2-bit divider circuit. The two bits input for one number are X0, X1, and Y0, and Y1 is for another number. In the circuit, the Z0, Z1, Z2 & Z3 signify the representation of binary form for the quotient. The circuit is designed with logic gates like AND & Ex-OR gates which are shown in the above figure. The most popular logic gate operation can be found in different circuits like multiplexer (Mux) & demultiplexer (Demux).

What is a trinary code?

Ternary coding is very efficient mathematically as compared to binary coding. In computation, this coding is used little because for binary processing, technology is previously established & the ternary coding implementation is more difficult, however, remains related within algorithms that utilize decision trees as well as in communications.

What is the short division method?

The short division method is also called the bus stop method. This method is frequently used for dividing large numbers like dividing up to 4 digits numbers through a 1-digit number.

What is the division algorithm method?

The division algorithm method simply says when a number ‘x’ is divided through a number ‘y’ & gives the ‘q’ quotient & the remainder to be ‘z’ then x = yq + z where 0 ≤ z < y. This is also called “Euclid’s division lemma”. In simple words, it can be signified in simple words like Dividend = Divisor* Quotient + Remainder.

Thus, there are four kinds of arithmetic operations that occur within binary arithmetic binary addition, subtraction, multiplication, and division. Among them, the binary division or long division is mainly used to divide two numbers and these numbers are signified in binary form. The working of binary division is the same as the long division technique within the decimal system. Here is a question for you, what is binary addition?

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