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Operations in other Bases

Reference > Mathematics > Number Theory > Bases

How 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 4sixteen + 7sixteen is Bsixteen, and Asixteen x 4sixteen is 28sixteen, 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.

Calculate the value of 23fifteen + 11fifteen. 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 34fifteen.

Calculate the value of 132twelve - 1020three

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 122 + 3 x 12 +2 = 182
1 x 33 + 0 x 32 + 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.


Calculate 15six + 28nine
Calculate 5eight + 6eight + 7eight
Calculate 40five + 30five and give your answer in base six.
Calculate 111two + 1, and give your answer in base two.
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Converting to other BasesConverting to other Bases
Determining the BaseDetermining the Base

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