# Operations in other Bases

Reference > Mathematics > Number Theory > BasesHow can you perform arithmetic operations like addition, subtraction, etc. on numbers in other bases?

Well, I hate to tell you this, but unless you can train yourself to memorize math facts in other bases (and really, who wants to remember that 4_{sixteen} + 7_{sixteen} is B_{sixteen}, and A_{sixteen} x 4_{sixteen }is 28_{sixteen}, and all of the other math facts for base sixteen - plus the math facts for all the other bases!) the best option is to convert your numbers into base ten, perform the operation, and then convert them back.

**EXAMPLE**

Calculate the value of 23_{fifteen} + 11_{fifteen}. Write your answer in base fifteen.

2 x 15 + 3 = 33

1 x 15 + 1 = 16

33 + 16 = 49

Convert 49 (base ten) back into base fifteen using the process described in the previous page, and you find that the result is 34_{fifteen}.

**EXAMPLE**

Calculate the value of 132_{twelve} - 1020_{three}

Here it looks like the second number is larger than the first one (it has more digits) but in reality, it is not, because its place value is such a small number (three).

1 x 12^{2} + 3 x 12 +2 = 182

1 x 3^{3} + 0 x 3^{2} + 2 x 3 + 0 = 33

182 - 33 = 149

Since we haven't been asked to give the answer in a particular base, we will leave it as a base ten number.

## Questions

_{six}+ 28

_{nine}

_{nine}

_{two}

_{eight}+ 6

_{eight}+ 7

_{eight}

_{five}+ 30

_{five}and give your answer in base six.

_{two}+ 1, and give your answer in base two.