Question

4. Using the switching algebra theorems minimize the following logic functions:

a. F = WXYZ(WXYZ’ + WX’YZ + W’XYZ + WXY’Z)
b. F = XY + X’Y + YZ +Y’Z

c. F = A’C’ + A’BC + B’C
d. F = X + Y (Z + X + Z)

Answer 1

a). F = WXYZ ( WXYZ’ + WX’YZ + W’XYZ + WXY’Z )

=  WXYZ WXYZ’ +WXYZ WX’YZ + WXYZ W’XYZ + WXYZ WXY’Z )

= WXYZZ' + WXX'Z + XYZWW'+WXZYY'

= WXY (ZZ' )+ WZ (XX') + XYZ (WW'+)WXZ (YY' )

  = 0 + 0 + 0 +0

= 0

.............................................................................................................................
b). F = XY + X’Y + YZ +Y’Z

= XY +X'Y + Z( Y+Y' )

= XY + X'Y + Z(1)

= XY + X'Y + Z

= Y(X+X') + Z

= Y(1) +Z [ Since A+ A'=1 ]

= Y + Z

..........................................................................................................................................

c). F = A’C’ + A’BC + B’C

= A’C’ + A’BC + B’C(A+A')

= A'C' + A'BC + B'CA + B'CA'

  ..............................................................................................................................................

d). F = X + Y (Z + X + Z)

= X + YZ+ YX+YZ

= X + YZ +YX [ Since A + A = A ]

= X(1+Y) + YZ

= X(1) + YZ

= X + YZ