GATE 2007 EE

Question

A, B, C and D are input bits, and Y is the output bit in the XOR gate circuit of the figure below. Which of the following statements about the sum S of A, B, C, D and Y is correct?

(A) S is always either zero or odd

(B) S is always either zero or even

(C) S = 1 only if the sum of A, B, C and D is even

(D) S = 1 only if the sum of A, B, C and D is odd

Comments

Options C and D are confusing. Can some one help me out?

Answer 1

Answer is D. TRy making the Y 1. If sum will be odd means possible values are either sum is 1, 3 . try making sum 1. either  and b should be different or c and d should be different but one pair has to be zero. (0,1) (0,0) or (0,0)(1,0) then sum will be 1 like wise try for making 3. The y = 1 only when xor input are complement of each other. so D

Comments

So, should the option D be like  "Y" = 1 only if the sum of A, B, C and D is odd ?

Answer 2

Answer is D)

Answer 3

CORRECT OPTIONS : B,D

FOR OUTPUT Y=0 : 

AB(00) , CD(11) THEN HERE WE GET SUM=0 CARRY=1 AND EVEN

AB(00) , CD(00) THEN SUM IS 0 ;EVEN 

AB(01) , CD(01) SUM=0 , EVEN

AB(11) , CD(11) THEN SUM=0 FOR ALL THESE CASES SUM IS EITHER ZERO OR EVEN

FOR OUTPUT Y=1:

AB(00) , CD(10) SUM=1 AND ODD

AB(11) , CD(10) SUM=1 AND ODD 

             

            

Answer 4

Y = (A ⊕ B) ⊕ (C ⊕ D)

 

Y = 1, iff A ⊕ B is 1 and C ⊕ D is 0 or, A ⊕ B is 0 and C ⊕ D is 1

 

=> Y = 1 iff:

1) A = B' and C = D

=> A+B+C+D = 1 or, 3

=> S = 2 or, 4

or,

2) A = B and C = D'

=> A+B+C+D = 1 or, 3

=> S = 2 or, 4

 

Y = 0, iff A ⊕ B is 1 and C ⊕ D is 1 or, A ⊕ B is 0 and C ⊕ D is 0

 

=> Y = 0 iff:

1) A = B' and C = D'

=> A+B+C+D = 2

=> S = 2

or,

2) A = B and C = D

=> A+B+C+D = 0 or, 4

=> S = 0 or, 4

 

=> B)