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Which of the following expression remove hazard from : $xy+zx'$?

A. $xy+zx'$

B. $xy+zx'+wyz$

C. $xy+zx'+yz$

D. $xy+zx'+wz$
in Digital Logic by Active (1.1k points)
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1 Answer

+15 votes
Best answer

Fill $f(x,y,z)=xy+x'z$ in K-map

Hazard occurred because a variable and its complement passed through different number of logic operations. 

In other words, if a variable and its complement are present in different product terms, may cause Hazards. 

Here it is variable $x$, that may cause Hazard. 

So make an extra pair in K-map that doesn't contain variable $x$.

so $f(x,y,z)=xy+x'z +yz$ is Hazard Free.

by Veteran (57k points)
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but we still have x and x' in expression.

yes, but in any case we have one more product term yz that will be unaffected if x cause hazard.
K thank you
C)  Using Redundant theorem

 AB + A'C + BC = AB + A'C + BC(A+A')

                       = AB + A'C + ABC + A'BC

                     = AB(1 + C) + A'C(1 + B)

                     =AB.1 + A'C.1      [A +1 = 1  ]

                   =AB + A'C



F = XY + ZX' + YZ.1

F = XY + ZX' + YZ(X+X')      [   A +A' = 1  ]

F= XY + ZX' + XYZ + X'YZ

F = XY(1 + Z) + ZX'(1 + Y)

F = XY.1 + ZX'.1          [A +1 = 1  ]

F = XY + ZX'
Sir can u please explain the concept in some more detail or please tell some book or online resource from where I can learn this
basic is given in Digital design by Morris Mano. I think you can find ebook easily.
Sir, I could not find it in Morris Mano book.. Is there any book from where I can read it
Which chapter in morris mano?I cant find this topic
Chapter 9.
It is not there is chapter 9... Which edition of the book are u using?

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