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The simultaneous equations on the Boolean variables x, y, z and w,

$$x + y + z = 1 \\xy = 0\\xz + w = 1\\xy + \bar{z}\bar{w} = 0$$

have the following solution for x, y, z and w, respectively:

  1. 0 1 0 0
  2. 1 1 0 1
  3. 1 0 1 1
  4. 1 0 0 0

 

asked in Digital Logic by Veteran (68.8k points)
edited by | 878 views
Although option rejection is good approach. But 4 variable k-map could be used to find all solutions(means cells where one will come for all expression) like 1010 is also a solution.

3 Answers

+16 votes
Best answer
Take each option one by one and try to put the values of x ,y ,z , and w in question

1.  

0+1+0 =1

0.1 =0

0.0+0 =0  (went wrong)       ....SO this is not the right option

2.

1+1+0 =1

1.1 =1 (went wrong)           ....not right

3 .

1+0+1 =1

1.0 =0

1.1+1=1

1.0 +1.0 =0  .....This is the right option
answered by Veteran (44.3k points)
selected by
+7 votes
Answer: C
answered by Veteran (35.8k points)
x + y + z =  1 + 0 + 1 = 0 ? only right
Got it. basic OR gate properties
0 votes
Answer -    C. 1 0 1 1   * think without ink*
answered by Loyal (3.3k points)


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