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simplycoder • Mar 17, 2012

# Ambigiuous Question

Hi all,

Recently I came across this question.
33/11=3 is true in which base?
a)10 b)2 c)both d)none

The answer given to this was both which is satisfactory when we use the equation which relates the number with place values and coefficients. But then can base 2 have '3' as its symbol? and even if it has, would the arithmatic be the same and valid as in base 2. First of all can 3 be a part of binary system as a symbol.

What are your views on this?

Explanation:
33 in binary code is 100001
11 in binary code is 1011
Let's perform the division of 100001 by 1011

Binary Division:
..........________
1011 ) 100001 ( 11
.............1011
...........______
.............01011
...............1011
...........______
...............0000

Here we get quotient as 11 which is 3 in decimal and 0000 as the remainder.
So 33 / 11 = 3 both in decimal and binary.
simplycoder
But then can base 2 have '3' as its symbol? and even if it has, would the arithmatic be the same and valid as in base 2. First of all can 3 be a part of binary system as a symbol.

What are your views on this?
I don't think 3 can be part of binary system, it can be represented in binary code.
silverscorpion • Mar 19, 2012
33/11 is 3 in any number system, if we convert them to that system first.

33 in base 5 is 113, and
11 in base 5 is 21

115/21 in base 5 will be

_____​
21) 113 ( 3
113​
_____​
0​

So, regardless of what base we use, it will always hold true. But the question does not ask that, I think. If anything, it might be a mistake and the choice should have been some other number instead of 2.. like 6 or 7, for example. In that case, we should convert both 33 and 11 to the appropriate base and see if it is indeed correct.