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GATE and UGC NET solve

UGC NET: 2014 (J2) Q: 18

Which of the following statement(s) is (are) not correct?

i) The 2’s complement of 0 is 0

ii) In 2’s complement, the left-most bit cannot be used to express a quantity.

iii) For an n-bit word (2’s complement) which includes the sign bit, there are 2n – 1 positive integer, 2n + 1 negative integers, and one 0 for a total of 2n unique states.

iv) In 2’s complement the significant information is contained in the 1’s positive numbers and 0’s of the negative information.

a) i and iv       

b) i and ii       

c) iii   

d) iv

Before seeing the answer please follow chapter: 

Signed representation by 2’s Complement

Solution:

(i) → Correct

So, the 2’s complement of 0 is 0

(ii) → Correct

Because the left-most bit is the sign bit. If it is 1, then the number is negative, otherwise, positive.

(iii) → Incorrect

So, 

And one 0.

(iv) → Correct

As significant information is contained in the 1’s of the positive numbers and the 0’s of the negative numbers.

∴ Answer: Option (c) as, (iii) is not correct.

Q. 3.  GATE CS 2004

Let A = 11111010 and B = 00001010 be two 8 bit 2´s complement numbers. Their product in 2´s complement is

(A) 11000100                                       

(B) 10011100

(C) 10100101

(D) 11010101

Before seeing the answer please follow chapter: 

Signed representation by 2’s Complement

Solution:

[∴ In 2´s complement, the sign bit is copied in all extended positions].

Since options are given in the 8-bit form.

So, equivalent result in 8 bits will be

UGC NET: 2012 (J2): Q: 35

If an integer needs two bytes of storage, then the maximum value of a signed integer is

Before  seeing  the answer please follow chapter: Signed Number representation

Solution:

2 byte = 16 bit

Now, range of 16 bit signed representation

Q. GATE CS 2003

Assuming all numbers are in 2´s complement representation, which of the following numbers is divisible by 11111011?

(A) 11100111                                       

(B) 11100100 

(C) 11010111 

(D) 11011011                                      

Solution:

∴ Option (A) is correct

Q. 6. UGC NET CS 2018 JULY-II

Perform the following operation for the binary equivalent of the decimal numbers 

The solution is in 8 bit.

Representation is:

(A) 11100011                                       

(B) 00011101 

(C) 10011101

(D) 11110011

Solution:

∴ Option (A) is correct