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How do you simplify the following boolean expressions: Y3= X3' X2 X1 X0' + X3' X2...

How do you simplify the following boolean expressions:

Y3= X3' X2 X1 X0' + X3' X2 X1 X0 + X3 X2 X1 X0' +X3X2X1X0

Y2 = X3' X2 X1' X0' + X3' X2 X1' X0 + X3 X2 X1' X0' + X3 X2 X1' X0 +  X3 X2' X1' X0' + X3 X2' X1' X0 + X3 X2' X1 X0' + X3 X2' X1 X0

Y1 = X3' X2' X1 X0' + X3' X2' X1 X0 + X3' X2 X1 X0' + X3' X2 X1 X0 +  X3 X2' X1' X0' + X3 X2' X1' X0 + X3 X2 X1' X0' + X3 X2 X1' X0

Y0 = X3' X2' X1' X0 + X3' X2' X1 X0 + X3' X2 X1' X0 + X3' X2 X1 X0 +  X3 X2' X1' X0 + X3 X2' X1 X0 + X3 X2 X1' X0 + X3 X2 X1 X0

Solutions

Expert Solution

Boolean expressions can be simplified by using boolean laws

Y3=X3'X2X1X0'+X3'X2X1X0+X3X2X1X0' +X3X2X1X0

   =X3'X2X1(X0'+X0)+X3X2X1(X0'+X0)

   =X3'X2X1(1)+X3X2X1(1) (A+A'=1)

   =X2X1(X3'+X3)

   =X2X1(1)

=X2X1

Y2 = X3'X2X1'X0' +X3'X2X1'X0 + X3X2X1'X0' + X3X2X1'X0 +  X3X2'X1'X0' + X3X2'X1'X0 + X3X2'X1X0' + X3X2'X1X0

   =X3'X2X1'(X0'+X0)+X3X2X1'(X0'+X0)+X3X2'X1'(X0'+X0)+X3X2'X1(X0'+X0) (A+A'=1)

=X3'X2X1'+X3X2X1'+X3X2'X1'+X3X2'X1

   =X2X1'(X3'+X3)+X3X2'(X1'+X1)

   =X2X1'(1)+X3X2'(1)

   =X2X1'+X3X2'

Y1= X3' X2' X1 X0' + X3' X2' X1 X0 + X3' X2 X1 X0' + X3' X2 X1 X0 +  X3 X2' X1' X0' + X3 X2' X1' X0 + X3 X2 X1' X0' + X3 X2 X1' X0

=X3'X2'X1(X0'+X0)+X3'X2X1(X0'+X0)+X3X2'X1'(X0'+X0)+X3X2X1'(X0'+X0)

   =X3'X2'X1+X3'X2X1+X3X2'X1'+X3X2X1'

   =X3'X1(X2'+X2)+X3X1'(X2'+X2)

   =X3'X1+X3X1' (EXCLUSIVE-OR OF X1 AND X3)

Y0=X3' X2' X1' X0 + X3' X2' X1 X0 + X3' X2 X1' X0 + X3' X2 X1 X0 +  X3 X2' X1' X0 + X3 X2' X1 X0 + X3 X2 X1' X0 + X3 X2 X1 X0

   =X3'X2'X0(X1'+X1)+X3'X2X0(X1'+X1)+X3X2'X0(X1'+X1)+X3X2X0(X1'+X1)

   =X3'X0(X2'+X2)+X3X0(X2'+X2)

   =X3'X0+X3X0

   =X0(X3+X3')

=X0

venereology answered 1 month ago
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