# Base conversion and equations [closed]

I am studying for an exam in my course, and I will certainly have a question of the kind:

In what base is the equation written, for example:

42-3=36


Another example:

(8*5+11)/4=12


I am wondering how to approach this kind of exercises, and how to solve them. I know how to convert from one base to another, but is there a method to solve these equations?

## closed as off-topic by Matt Young, Scott Seidman, Leon Heller, Phil Frost, m.AlinJun 23 '14 at 20:16

• This question does not appear to be about electronics design within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• This question appears to be off-topic because it is about math, not EE. – Matt Young Jun 23 '14 at 19:44
• @MattYoung, Actually I have to solve this question in a digital systems course, so I figuered it would be helpful to put it here. – Alan Jun 23 '14 at 19:48
• @Tut not everything that is used in electronics is on topic, and this question is not on topic if you look at the help center. – Keelan Dec 16 '14 at 13:09

Call the base "N". Then write the equation in base conversion form: The first one being:

4*N + 2 - 3 = 3*N + 6

Then solve for N

In general, digits in the second column (from the right) are multiplied by N, digits in the third column would be multiplied by $N^2$, digits in the fourth column would be multiplied by $N^3$, etc.

• thank you. Can you, please, explain why did you choose to put the N after the 4 and the 3? and what does the digit 7 represent? @Tut – Alan Jun 23 '14 at 19:52
• I think you mean 4*N + 2 - 3 = 3*N + 6 which is easier to simplify... – Brian Drummond Jun 23 '14 at 19:55
• Your question asked to find what base the equations are written. The value of N is the base. The 4 and the 3 are in the second column so are multiplied by N. If you had a three column number, you would multiply that digit by N squared, etc. – Tut Jun 23 '14 at 19:57
• The 7 was a mistake. Alan, do you know how the decimal system works insofar as the columns and their values? The ones column has a value of 10^0, the tens a value of 10^1, the hundreds a value of 10^2 .. and it continues. The N here represents the unknown base (10 in my example). – sherrellbc Jun 23 '14 at 19:57
• @BrianDrummond Ooops! I got a little careless in the rush to get my answer out :-) – Tut Jun 23 '14 at 20:01

Do note that the the base is going to at least be 1 integral number larger than the largest value seen in the expression. For example,

42 - 3 = 36

It at least of base >= 7.

This slipped my mind. I was thinking about logs for some reason. Tut had it first.

(4*x) + (2) - (3) = (3*x) + (6)

4x + 2 - 3 = 3x + 6

x = 7

Therefore, base 7

• thank you. I thought that the only way to do it is by trial and error. If I understand your example, than if I have an equation like 12=8, than the base is at least 6? – Alan Jun 23 '14 at 19:46
• At least of base 9 in that case. Actually, check out Tuts answer above. You can actually analytically solve in that way. – sherrellbc Jun 23 '14 at 19:49
• No - in 12 = 8, the base must be at least 9 - the base must be at least one count larger than the largest digit used. – Peter Bennett Jun 23 '14 at 19:49