How can you add numbers in base n?

Answer 1

Easy solution

1. Convert numbers to base 10

2. Add

3. Convert result to base n

To add without converting, follow these steps Adding 2 Numbers in a Different Base:

A. Adding numbers in a different base is similar to adding numbers in base 10.

1. Add the one's digits first like you would in base 10.

2. If the number is less than the base, write it down. If the number is greater than

or equal to the base, you must carry. So find the remainder after dividing by

the base and write it down (i.e. n MOD b) and to find the number you should

carry, find out how many times b will go into n (i.e. n DIV b).

3. Continue adding the next digits as described in step 2 until all numbers are

added. Don't forget to add in any carried numbers.

4. Note: You must add the digits from the right to left. In other words, add the

ones digit first, followed by the tens digit, and so on.

Ex [1] 143

5

+ 41

5

=_________

5

.

a. 3 + 1 = 4. Since 4 is less than 5, write it down.

b. 4 + 4 = 8. Since 8 is greater than 5, we must carry. 8 Mod 5 = 3.

Write down 3. 8 DIV 5 = 1. Carry the *1.

c. 1 + *1 = 2. Since 2 is less than 5, write it down.

d. The answer is 234.

Ex [2] 222

3

+ 121

3

+ 220

3

=________

3

.

a. 2 + 1 + 0 = 3. Since 3 is equal to 3, we must carry. 3 MOD 3 = 0.

Write this down. 3 DIV 3 = 1. Carry *1.

b. 2 + 2 + 2 = 6 + *1 = 7. Since 7 is greater than 3, we must carry.

7 MOD 3 = 1. Write down 1. 7 DIV 3 = 2. Carry *2.

c. 2 + 1 + 2 = 5 + *2 = 7. Since 7 is greater than 3, we must carry.

7 MOD 3 = 1. Write down 1. 7 DIV 3 = 2. Since there are no

more numbers we can just write down 2.

d. The answer is 2110.