The binary subtraction questions and answers can help students to more easily comprehend the concept of “Binary subtraction.” Students may quickly understand the concept by using the questions that are provided here. Additionally, we’ve provided some practice questions to aid with their understanding. You can double-check your solution by referring to the in-depth justifications we offer on our web page for each question. Visit this page for further details on binary subtraction.

Binary Subtraction Questions with Solutions

1. Subtract 1000₂ from 11111₂, and justify the answer.

Solution:

Given: We have to subtract 1000₂ from 11111₂

Step 1: Now, arrange the given binary numbers as given below:

11111

 1000

(-)

_____

_____

Step 2: Now, subtract the given binary numbers using the rules from right to left.

Since, 1 – 0 = 1 and 1 – 1 = 0, we get;

11111

 1000

(-)

_____

10111

_____

Step 3: Hence, the required solution is 10111₂

I.e., 11111₂ – 1000₂ is 10111₂

Verification:

The decimal equivalent of 11111₂ = 31

The decimal equivalent of 1000₂ = 8

Hence, 31 – 8 = 23, which is equivalent to 10111₂.

Hence, verified.

2. Subtract the binary numbers: 1011000₂ – 111000₂

Solution:

Given: 1011000₂ – 111000₂

Step 1: Arrange the given binary numbers as follows:

1011000

  111000

(-)

________

________

Step 2: Using binary subtraction rules, such as 1 – 0 = 1, 1 – 1 = 0, 0 – 0 = 0, 0 – 1 = 1 (with borrow), we get the following:

1011000

  111000

(-)

________

100000

________

Step 3: Hence, 1011000₂ – 111000₂ = 100000₂

3. Subtract the binary numbers: 1110001₂ – 110010₂.

Solution:

Given: 1110001₂ – 110010₂

Step 1:

1110001

 110010

(-)

_______

_______

Step 2:

Using binary subtraction rules, we get

1110001

 110010

(-)

_______

111111

______

Step 3: The required solution is 111111₂

Therefore, 1110001₂ – 110010₂ is 111111₂.

4. Subtract 1000100₂ from 1011000₂

Solution: 10100

Given: 1011000₂ – 1000100₂

Step 1:

1011000

1000100

(-)

_______

_______

Step 2: Use the binary subtraction rules,

1011000

1000100

(-)

_______

   10100

________

Step 3: Hence, the difference is 10100₂

Hence, the 1000100₂ from 1011000₂ is 10100₂.

5. Find the difference: 1100100₂ – 110010₂, and verify your answer.

Solution:

Given: 1100100₂ – 110010₂

Step 1: Write the given numbers as follows:

1100100

 110010

(-)

______

______

Step 2: Using the binary subtraction rules, we can find the difference between two binary numbers.

1100100

  110010

(-)

______

110010

______

Step 3: Therefore, the required difference is 110010₂.

Hence, 1100100₂ – 110010₂ is 110010₂.

Verification:

The decimal equivalent of 1100100₂ is 100.

The decimal equivalent of 110010₂ is 50.

Thus, 1100100₂ – 110010₂ is 110010₂, which is equal to 50.

I.e., 100 – 50 = 50.

6. Subtract 1101111₂ – 1011011₂ using 1’s complement.

Solution:

Given: 1101111₂ – 1011011₂

Step 1: Take the one’s complement of the subtrahend (1011011₂). Hence, we get 0100100₂.

Step 2: Now, add the result obtained in step 1 with the minuend (1101111)_2.

Step 3: Arrange the binary numbers as follows and add them.

0100100

1101111

(+)

________

10010011

________

Here, the carry over is 1, which is the leftmost digit of the sum.

Step 4: As, we have the carry over 1, add 1 with the result 0010011₂.

0010011

(+)        1

_______

10100

________

Step 5: Therefore, the required solution is 10100₂.

I.e., 1101111₂ – 1011011₂ = 10100₂.

7. Subtract 101110₂ – 100100₂ using 1’s complement.

Solution:

Given: 101110₂ – 100100₂

Step 1: Take the one’s complement of 100100₂. Hence, we get 011011₂.

Step 2: Now, add the result with the minuend 101110₂

Step 3: Arrange the binary numbers as follows and add them.

011011

101110

(+)

________

1001001

________

Step 4: Here, we have the carry over 1, so, add 1 with the result 001001₂.

001001

(+)      1

_______

001010

_______

Step 5: Therefore, the required solution is 1010₂.

I.e., 101110₂ – 100100₂ = 1010₂.

8. Subtract the binary numbers: 11111010₂ – 101000₂

Solution:

Given: 11111010₂ – 101000₂

Step 1: Arrange the given binary numbers as follows:

11111010

  101000

(-)

_________

_________

Step 2: Use the binary subtraction rules to get the difference.

11111010

  101000

(-)

_________

11010010

_________

Step 3: Hence, the required difference is 11010010₂.

I.e., 11111010₂ – 101000₂ = 11010010₂,

9. Find the difference between binary numbers 110101₂ – 100010₂ using 1’s complement.

Solution:

Given: 110101₂ – 100010₂

Step 1: Take the one’s complement of the 100010₂. Hence, we get 011101₂.

Step 2: Now, add the result with the minuend 110101_2.

Step 3: Now, add the obtained binary numbers

011101

110101

(+)

________

1010010

________

Step 4: Here, the carry over is 1, and hence add 1 with 010010₂

010010

(+)      1

_______

010011

________

Step 5: Therefore, the required solution is 010011₂.

I.e., 110101₂ – 100010₂ = 010011₂.

10. Subtract 1001100₂ – 110₂ using rules of binary subtraction. Also justify your answer.

Solution: 76 – 6

Given: 1001100₂ – 110₂

Step 1: Arrange the binary numbers as follows:

1001100

(-)    110

_______

_______

Step 2: Using the rules of binary subtraction, we get

1001100

(-)    110

_______

01000110

_______

Step 3: Hence, the required solution is 01000110₂

Therefore, 1001100₂ – 110₂ = 01000110₂

Justification:

The decimal equivalent of 1001100₂ is 76.

The decimal equivalent of 110₂ is 6.

Hence, 76 – 6 = 70, which is equivalent 01000110₂

Hence, verified.

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Practice Questions

Solve the following binary subtraction questions:

1. Subtract the binary number 110110₂ from 1100011₂.
2. Subtract the numbers using the binary subtraction rules: 1001000₂ – 100100₂.
3. Subtract the binary numbers using 1’s complement: 1111100₂ – 111110₂.

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