Addition in base five

Addition in base five is similar to addition in base 10 and it is not complicated once you understand the basics

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

Base 5 uses 0, 1, 2, 3, and 4

Adding in base 10:

7 + 5 = 12 = 10 + 2 The 2 is put in the place value where you are adding 7 and 5

The 10 is carried over to the next place value on the left of 7 and 5

Usually, we use 1 to represent the 10

Now, if the number is less than 10, just write it down in the same place where you are doing the addition

Nothing really has changed when adding in base five

For example, if 4 and 3 are already in base 5 and you want to add them, what would you do?

4 + 3 = 7 = 5 + 2

Put 2 in the same place as 4 and 3

Carry the 5 over to the next place value on the left of 4 and 3

Again, we use 1 to represent the 5

Let's practice now with some examples


Example #1:Addition in base five with no carry

To avoid confusion with base 10, we put a 5 next to each number

However, it is clear to you that the addition is being done in base five, there is no need to write down the 5

Add: 221₅ + 123₅


   2 2 1₅
   1 2 3₅
_______________________
   3 4 4₅


Notice that the addition above was easy so far. Something more interesting to follow!

Example #2: Addition in base five with carry

Add: 432₅ + 341₅



1 1
           4 3 2₅
          3 4 1₅
    ___________________________
1 3 2 3₅


Explanation:

2 + 1 = 3. It is less than 5, so there is no carry. Just write 3 down

4 + 3 = 7 = 5 + 2

Write 2 down and carry a 5. However, use 1 to represent 5 just like in base 10

1 + 4 + 3 = 8 = 5 + 3

Write 3 down and carry a 1 again

The last one all the way to the left that was carried over can be brought down now.

Example #3: With carry

Add: 124214₅ + 403312₅



1    1 1    1
           1 2 4 2 1 4₅
          4 0 3 3 1 2₅
  _____________________________________________
1 0 3 3 0 3 1₅


Explanation:

4 + 2 = 6 = 5 + 1. Put 1 down and carry 1

1 + 1 + 1 = 3. Put 3 down

2 + 3 = 5 = 5 + 0. Write 0 down and carry a 1

1 + 4 + 3 = 8 = 5 + 3. Write 3 down and carry a 1

1 + 2 + 0 = 3. Write 3 down.

1 + 4 = 5 = 5 + 0. Write 0 down and carry a 1

The last one all the way to the left that was carried over can be brought down now.