GATE Overflow Test Series | Digital Logic | Test 1 | Question: 3

Question

In which of the following signed number representations we have more positive numbers than negative numbers?

• A. $1's$ Complement Representation
• B. $2's$ Complement Representation
• C. Sign magnitude Representation
• D. None of the Above

Comments

@gatecse

if question says

in which representation we have more negative  numbers than positivenumbers?

then answer must be 2’s complement

Kindly correct if i missed something.

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val_pro20

Yes, you are right.

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@val_pro20 No. 2’s complement also has an equal number of positive and negative numbers.

ex: for 3 bit : (-4,-3,-2,-1) , (0,1,2,3) . So, 4 positive numbers and 4 negative numbers.

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0 is neither positive nor negative 

so, we have more negative numbers than positive numbers in 2’s complement representation.
 

Answer 1

With $n$ bits we can represent $2^n$ distinct numbers. In both $1's$ complement as well as sign magnitude representations we have $2$ zeroes, and the rest $2^n -2$ numbers are used to represent equal number of positive and negative numbers.
     
     In $2's$ complement representation there is a single zero. The rest $2^n-1$ numbers are split to $2^{n-1}-1$ positive numbers and $2^{n-1}$ negative numbers.
     
     So, in none of the given representations we have more positive numbers than negative numbers.
     
     Correct Answer: D.