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Direction: In a number system there are symbols namely @ and #. ‘0’ is represented by ‘@’and ‘1’ is represented by ‘#’. Subsequently,
‘2’ is represented by ‘#@’.
‘3’ is represented by ‘##’
‘4’ is represented by ‘#@@’
‘5’ is represented by ‘#@#’
‘6’ is represented by ‘##@’
Based, on the above pattern, answer the question that follows-
Q. Which of the following will represent code for ‘23’?
  • a)
    #$#@#
  • b)
    #@###
  • c)
    @##@#
  • d)
    ##@@#
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Direction: In a number system there are symbols namely @ and #. ‘0’ i...
According to the given information-
To get the equivalent of 23, we use the method of successive division by 2-
Now the code- 10111
On replacing ‘1’ and ‘0’ by ‘#’ and ‘@’ respectively-
The code for → ‘23’ → ‘10111’ → #@###
So, the code for 23 is ‘#@###’.
Hence, the correct option is (B).
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Community Answer
Direction: In a number system there are symbols namely @ and #. ‘0’ i...
Understanding the Symbol System
In the given number system, symbols are used to represent binary digits:
- ‘0’ is represented by ‘@’
- ‘1’ is represented by ‘#’
- Numbers greater than ‘1’ are constructed using these symbols in a specific pattern.
Breaking Down the Representation
Here’s how numbers are represented:
- ‘2’ is represented by ‘#@’
- ‘3’ is represented by ‘##’
- ‘4’ is represented by ‘#@@’
- ‘5’ is represented by ‘#@#’
- ‘6’ is represented by ‘##@’
Finding the Code for ‘23’
To represent the number ‘23’, we need to break it down into its binary representation:
1. Binary Conversion: The decimal number ‘23’ is equivalent to binary ‘10111’.
2. Symbol Representation:
- Each binary digit can be translated using the defined symbols:
- ‘1’ = ‘#’
- ‘0’ = ‘@’
3. Constructing the Code:
- From the binary ‘10111’, we translate it as follows:
- First digit ‘1’ → ‘#’
- Second digit ‘0’ → ‘@’
- Third digit ‘1’ → ‘#’
- Fourth digit ‘1’ → ‘#’
- Fifth digit ‘1’ → ‘#’
- Combining these gives: #@###
Conclusion
Thus, the code representing ‘23’ is #@###, which corresponds to option 'B'.
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