Binary Division Questions

Let us first understand what a Binary system is, before jumping to the binary division questions.

In our day-to-day activities, we use a number system that is termed a decimal system, which has 10 numbers, starting from 0 to 9. It is also called the base 10. Now the Binary system is another number system where only 0 and 1 are used. It is also called the base 2 system, as only 2 numbers are used. The next question is why or where we use this system. Even though the decimal system is very helpful for many mathematical operations, it has its own demerits. Binary systems are mainly used in the computer world. All basic internal operations work on the 2 numbers 0 and 1, termed as bits. You can find a detailed explanation of the binary system here.

This article is more about the problems that deal with Binary division. Hence it is important that we revisit the rules of binary division.

Since there are only 2 digits in the binary system, the combination of divisors is only 4. The possible 4 divisors and their rules are:

1. Divide 1 by 0 ⇒ 1 ÷ 0 = Not defined/invalid
2. Divide 1 by 1 ⇒ 1 ÷ 1 = 1
3. Divide 0 by 1 ⇒ 0 ÷ 1 = 0
4. Divide 0 by 0 ⇒ 0 ÷ 0 = Not defined/invalid

You can refer to more on division rules at Binary Division Rules.

Binary Division Questions With Solutions

Here are a few Binary division questions with steps that lead to the answer.

Question 1:

Divide 100₂ ÷ 10₂

Solution:

When 100₂ ÷ 10₂ the quotient is 10₂

Question 2:

Convert the decimal numbers into binary and divide in binary

55 ÷ 5

Solution:

Given decimal numbers are 55 and 5. The division of 55 and 5 gives us 11 as the quotient in the decimal system. Let us convert 55 and 5 into binary and then divide them into binary.

Conversion of 55

55₁₀ = 110111₂

Conversion of 5

5₁₀ = 101₂

Conversion of 11

11₁₀ = 1011₂

Dividing 110111₂ by 101₂

The quotient is 1011₂ which is the same as 11₁₀.

Question 3:

Divide 1000₂ by 10₂

Solution:

When 1000₂ is divided by 10₂, the quotient is 100₂

Question 4:

When 11110 is divided by 10, the quotient is 1111. Prove this statement.

Solution:

Yes. The statement is true. When 11110 is divided by 10, the quotient is 1111

Question 5:

Divide 1010001₂ by 1001₂

Solution:

When 1010001₂ is divided by 1001₂ the quotient is 1001₂.

Question 6:

Show that 35₁₀ divided by 7₁₀ is 5₁₀ by converting 35, 7 and 5 into binary numbers and by binary division.

Solution:

Converting 35, 7 and 5 into binary.

1. Converting 35 into binary

35₁₀ = 100011₂

1. Converting 7 into binary

7₁₀ = 111₂

1. Converting 5 into binary

5₁₀ = 101₂

When 35₁₀ (100011₂) is divided by 7₁₀ (111₂) the quotient is 5₁₀ (101₂).

Question 7:

Divide 110010000₂ by 10100₂

Solution:

When 110010000₂ is divided by 10100₂, the quotient is 10100₂. Check the division in the image below.

Question 8:

Divide 110110₂ by 10010₂

Solution:

When 110110₂ is divided by 10010₂ the quotient is 11

Question 9:

Prove that 110000₂ divided by 1000₂ is 110₂. Prove this statement by converting binary numbers into decimal systems.

Solution:

Given numbers are

110000₂ = 1 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 0 × 2² + 0 × 2¹ + 0 × 2⁰

= 32 + 16 + 0 + 0 + 0 + 0

= 48

1000₂ = 1 × 2³ + 0 × 2² + 0 × 2¹ + 0 × 2⁰

= 8 + 0 + 0 + 0

= 8

110₂ = 1 × 2² + 1 × 2¹ + 0 × 2⁰

= 4 + 2 + 0

= 6

48 divided by 8 is 6. This proves the statement that when 110000₂ is divided by 1000₂ the quotient is 110₂

Question 10:

Divide 10000011₂ by 10₂

Solution:

When 10000011₂ is divided by 10₂, the quotient is 1000001.1₂

Note that 10000011₂ is not completely divisible by 10₂, we need to place a decimal point to complete the division.

Related Articles:

• Number Systems
• Binary operations
• Binary to Decimal
• Binary Addition
• Binary Calculator

Practice Questions on Binary Division

1. Solve the following binary division
   • 101010₂ ÷ 101
   • 111000₂ ÷ 111
   • 1110₂ ÷ 110
   • 1001₂ ÷ 101
   • 110011₂ ÷ 111
2. Solve the following binary division
   • 1100₂÷ 11
   • 1010₂÷ 10
   • 1001₂÷ 100
   • 0011₂÷ 1110
   • 0101₂÷ 1010
3. Follow the below steps to solve the given problems
4. Divide the following decimal numbers
5. Convert the decimal numbers into binary
6. Divide the binary numbers
7. Compare the results obtained by the division of decimal and binary.

Problem 1: 125 ÷ 5

Problem 2: 13456 ÷ 2

Problem 3: 7890 ÷ 10

Problem 4: 166782 ÷ 11