Addition in base two


Addition in base two is similar to addition in base ten. Although there is a difference, it is not that hard to add in base 2






Base 10 uses 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

The place value for base 10 is shown below:

Hundred thousands
Ten thousands
Thousands
Hundreds
tens
ones
8
7
0
4
9
7


However, a deep understanding of addition in base 10 will help you understand deeply addition in base two

Add 978 and 856 in base 10

  1     1       1
          9 7 8
          8 5 6
_________________________
1 8 3 4 


Explanation:

Add the numbers in the ones place: 8 + 6 = 14 = 10 + 4

Write 4 in the ones place and carry the 10 to the tens place. You can just use a 1 to represent the 10 (shown in red)

Add the numbers in the tens place

1 ten + 7 tens + 5 tens = 13 tens = 10 tens + 3 tens = 100 + 3 tens

Write 3 tens in the tens place and carry the 100 to the hundreds place. You can just use a 1 to represent the 100 (shown in green)

Add the numbers in the hundreds place

1 hundred + 9 hundreds + 8 hundreds = 10 hundreds + 8 hundreds = 1000 + 8 hundreds

Write 8 hundreds in the hundreds place and carry the 1000 to the thousands place. You can just use a 1 to represent the 1000 (shown in black) Bring down the 1 shown in black and you are done!




Addition in base two

We will follow the exact same pattern above to show how to add in base 2


Base 2 uses 0 and 1

We show a place value for base 2 below:

Notice that the twos place in base 2 is the tens place in base 10

Thirty-twos
Sixteens
Eights
Fours
Twos
Ones
0
1
1
0
1
0


Let's practice now with some examples


Example #1:Addition in base two with carry

To avoid confusion with base 10, we put a 2 next to each number

However, it is clear to you that the addition is being done in base 2, there is no need to write down the 2

Add: 1012 + 1012


  1     1       1
       0 1 12
       1 0 12
___________________________
1 0 0 02


Explanation:

Add the numbers in the ones place: 1 + 1 = 2 = 2 + 0.

Write 0 in the ones place and carry the 2 to the twos place. You can just use a 1 to represent the 2 (shown in red)

Add the numbers in the twos place: 1 two + 1 two + 0 two = 2 twos = 4 = 4 + 0

Write 0 in the twos place and carry the 4 to the fours place. You can just a 1 to represent the 4 (shown in green)

Add the numbers in the fours place: 1 four + 0 four + 1 four = 2 fours = 8 = 8 + 0

Put 0 in the fours place and carry the 8 to the eights place. You can just put a 1 to represent the 8 (shown in black)

Bring down the 1 shown in black et voila!



Example #2:

Add: 11012 + 11012


   1    1                1
          1 1 0 12
          1 1 0 12
________________________________
1 1 0 1 02


Explanation:

Add the numbers in the ones place: 1 + 1 = 2 = 2 + 0.

Write 0 in the ones place and carry the 2 to the twos place. You can just use a 1 to represent the 2 (shown in red)

Add the numbers in the twos place: 1 two + 0 two + 0 two = 1 two

Write 1 two in the twos place.

Add the numbers in the fours place: 1 four + 1 four = 2 fours = 8 = 8 + 0

Put 0 in the fours place and carry the 8 to the eights place. You can just put a 1 to represent the 8 (shown in green)

Add the numbers in the eights place: 1 eight + 1 eight + eight = 2 eights + 1 eight = 16 + 1 eight

Write 1 eight in the eights place and carry the the 16 to the sixteens place. You can just use a 1 to represent the 16 (shown in black)

Bring down the 1 in the sixteens place shown in black et voila!

If you struggle to understand addition in base two, you may need to go back to the example I gave about base 10 and try your best to relate this to base two







Recent Articles

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz