Ambigiuous Question

simplycoder

simplycoder

@simplycoder-NsBEdD • Oct 22, 2024
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?
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  • Dancer_Engineer

    Dancer_Engineer

    @dancer-engineer-EJ8rGI • Mar 18, 2012

    (C) is the correct answer.

    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.
    0
  • Dancer_Engineer

    Dancer_Engineer

    @dancer-engineer-EJ8rGI • Mar 18, 2012

    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.
    0
  • silverscorpion

    silverscorpion

    @silverscorpion-iJKtdQ • Mar 18, 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.
    0