You are here:
  1. / iCalculator
  2. / Arithmetic
  3. / Decimal Number System
  4. / Binary Numbers

Menu

Math Lesson 1.7.4 - Operations with Binary Numbers

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

★★★★★ [ 3 Votes ]

Welcome to our Math lesson on Operations with Binary Numbers, this is the fourth lesson of our suite of math lessons covering the topic of Decimal Number System and Other Numbering Systems, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Operations with Binary Numbers

We can do all four basic operations with binary numbers in a similar way to operations we have discussed in the decimal system. Thus, for addition we can carry numbers but this time not when the sum of two digits is 10 or more but when it is 2 or more. Likewise, in subtraction we can borrow one unit from the place value on the right when the difference of two digits is not possible. The only difference is that this action does not increase the value of minuend digit by 10 but by 2.

Multiplication and division are also carried out in a similar way to decimal number system. Let's take an example for each operation.

Example 6

Complete the following operations with binary numbers and then prove the correctness of results through the corresponding decimal operations.

  1. 1110101 + 110011
  2. 1011010 - 1101
  3. 11110 × 101
  4. 100100 ÷ 1001

Solution 6

  1. For simplicity, we can complete the operations in columns as we did for decimal operations. We have Math Tutorials: Operations with Binary Numbers Example Proof:: 1110101 = 64 + 32 + 16 + 0 + 4 + 0 + 1 = 117; 110011 = 32 + 16 + 0 + 0 + 2 + 1 = 51. Thus, 117 + 51 = 168. On the other hand, 10101000 = 128 + 0 + 32 + 0 + 8 + 0 + 0 + 0 = 168. Hence, the two results obtained through different methods of calculation match.
  2. Again, we complete the operations in columns. We have Math Tutorials: Operations with Binary Numbers Example Proof:: 1011010 = 64 + 0 + 16 + 8 + 0 + 2 + 0 = 90; 1101 = 8 + 4 + 0 + 1 = 13. Thus, 90 - 13 = 77. On the other hand, 1001101 = 64 + 0 + 0 + 8 + 4 + 0 + 1 = 77. Hence, the two results obtained through different methods of calculations do match.
  3. We complete the multiplication in column in the same way as we did it for base 10 numbers. We have:Math Tutorials: Operations with Binary Numbers Example Proof:: 11110 = 16 + 8 + 4 + 2 + 0 = 30 and 101 = 4 + 0 + 1 = 5. Hence, 30 × 5 = 150 (in the decimal system). On the other hand, 10010110 = 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0 = 150. Hence, the two results obtained through different methods of calculations match.
  4. We complete the division using the method explained in tutorial 1.2. We haveMath Tutorials: Operations with Binary Numbers Example Hence, we have 100100 ÷ 1001 = 100.Proof:: 100100 = 32 + 0 + 0 + 4 + 0 + 0 = 36 and 1001 = 8 + 0 + 0 + 1 = 9. Thus, 36 ÷ 9 = 4. On the other hand, 100 = 4 + 0 + 0 = 4. So, our two results obtained through different methods of calculations match.

More Decimal Number System and Other Numbering Systems Lessons and Learning Resources

Arithmetic Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
1.7Decimal Number System and Other Numbering Systems
Lesson IDMath Lesson TitleLessonVideo
Lesson
1.7.1The Meaning of Decimal Number System. Writing a Number in Terms of Powers of Ten
1.7.2Place Values and Classes
1.7.3Other Number Systems - The Base 2 Number System
1.7.4Operations with Binary Numbers
1.7.5The Base 16 Number System

Whats next?

Enjoy the "Operations with Binary Numbers" math lesson? People who liked the "Decimal Number System and Other Numbering Systems lesson found the following resources useful:

  1. Binary Numbers Feedback. Helps other - Leave a rating for this binary numbers (see below)
  2. Arithmetic Math tutorial: Decimal Number System and Other Numbering Systems. Read the Decimal Number System and Other Numbering Systems math tutorial and build your math knowledge of Arithmetic
  3. Arithmetic Video tutorial: Decimal Number System and Other Numbering Systems. Watch or listen to the Decimal Number System and Other Numbering Systems video tutorial, a useful way to help you revise when travelling to and from school/college
  4. Arithmetic Revision Notes: Decimal Number System and Other Numbering Systems. Print the notes so you can revise the key points covered in the math tutorial for Decimal Number System and Other Numbering Systems
  5. Arithmetic Practice Questions: Decimal Number System and Other Numbering Systems. Test and improve your knowledge of Decimal Number System and Other Numbering Systems with example questins and answers
  6. Check your calculations for Arithmetic questions with our excellent Arithmetic calculators which contain full equations and calculations clearly displayed line by line. See the Arithmetic Calculators by iCalculator™ below.
  7. Continuing learning arithmetic - read our next math tutorial: Numbering Systems, a Historical View

Help others Learning Math just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

★★★★★ [ 3 Votes ]

We hope you found this Math tutorial "Decimal Number System and Other Numbering Systems" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.

Arithmetic Calculators by iCalculator™

© iCalculator™ 2009 - 2024 | Math Calculators | Privacy Policy | Terms of Use | Contact