# Binary Division

Binary division, like the other three binary operations, addition, subtraction, and multiplication, involves division involving the 2 binary numbers 0 and 1. Its algorithm is similar to decimal division, except it has only 2 numbers instead of 10.

Using only two numbers makes binary division even simpler than decimal division. However, like other binary operations, binary division follows some rules:

## Rules

The binary division follows the following 4 rules given in the table:

Thus, like the decimal system, division by 0 is meaningless in binary division.

## Steps

The binary division is usually done using the long division method. There can be 2 possible situations involving the same number of digits in the dividend and the divisor.

Note: The number of digits in the dividend is counted from the right.

### Case 1

Let us learn the steps by dividing the binary numbers 11111002 (the dividend) by 102 (the divisor.)

Step 1: Comparing the divisor with the dividend.

When the divisor is smaller than the dividend, we multiply the divisor with 1, and the result becomes the subtrahend. Finally, subtracting the subtrahend from the minuend gives us the remainder.

Here, on comparing the divisor with the dividend, we find the divisor 102 < 11001012, the dividend. Thus, the divisor will be multiplied by 1, resulting in the subtrahend.

Using the binary multiplication rule: 1 × 1 = 1, 1 × 0 = 0, 0 × 1 = 0, and 0 × 0 = 0, we get

Thus, 10 × 1 = 10 is the subtrahend.

Step 2: Subtracting the subtrahend 102 from the minuend 112 using the rules of binary subtraction: 0 – 1 = 1, 0 – 0 = 0, 1 – 1 = 0, and 1 – 0 = 0, we get (11 – 10) 1.

Step 3: Borrowing 1 from the next more significant bit and repeating step 1 and step 2 until the remainder becomes zero.

Thus, the binary division involving the divisor 102 and the dividend 11111002 is 1111102

We can verify our answer by finding the decimal equivalent of 1111102, which is 6210. Learn binary to decimal conversion here.

Divisor: 102 → 210

Divisor: 11111002 → 12410

Thus, the quotient is 12410 ÷ 210 = 6210

The decimal equivalent of 1111102 is also 6210. Thus, the answer is verified

### Case 2

Let us divide 100102, the dividend, with the divisor 112

Here, the divisor (11) is larger than the dividend (10), and thus, we place 0 in the quotient and then consider the second bit of the dividend, which is 100. Now, the divisor is smaller than the dividend and thus performs division similar to the previous method until we get 0 in the remainder.

Thus, the binary division involving the divisor 112 and the dividend 100102 is 1102

## Division with Remainder Other Than 0

However, in some divisions, there can be remainders greater than zero, as in the example shown:

## Solved Example

Divide 11102 ÷ 1112

Solution:

Give, the dividend = 1110 and the divisor = 111
Thus, the binary division involving the divisor 1112 and the dividend 11102 is 102