Table of Contents

Last modified on October 30th, 2023

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:

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

Dividend | Divisor | Result |
---|---|---|

0 | 1 | 0 |

1 | 1 | 1 |

1 | 0 | Meaningless |

0 | 0 | Meaningless |

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

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.

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 10_{2} and the dividend 1111100_{2} is 111110_{2}

We can verify our answer by finding the decimal equivalent of 111110_{2}, which is 62_{10}. Learn binary to decimal conversion here.

Divisor: 10_{2} → 2_{10}

Divisor: 1111100_{2 }→ 124_{10}

Thus, the quotient is 124_{10} ÷ 2_{10} = 62_{10}

The decimal equivalent of 111110_{2} is also 62_{10}. Thus, the answer is verified

Let us divide 10010_{2}, 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 11_{2} and the dividend 10010_{2} is 110_{2}

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

**Divide 1110 _{2} ÷ 111_{2}**

Solution:

Give, the dividend = 1110 and the divisor = 111

Thus, the binary division involving the divisor 111_{2} and the dividend 1110_{2} is 10_{2}