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

Adding in base 5:

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


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





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





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.