Question

Qc) Consider the following function F. х Y F N a) Derive the expression for the function F (Do not simplify F). b) Construct the truth table of F. c) Find expression for complement of F, F'.

Answer 1

F = (XY XOR (Y+Z)) XNOR Z'
F = (XY(Y+Z)' + (XY)'(Y+Z)) XNOR Z'
F = (XY(Y'Z') + (X'+Y')(Y+Z)) XNOR Z'
F = (0 + X'Y' + X'Z + 0 + Y'Z) XNOR Z'
F = (X'Y' + X'Z + Y'Z)Z' + (X'Y' + X'Z + Y'Z)'Z''
F = X'Y'Z + 0 + 0 + ((X'Y')'(X'Z)'(Y'Z)')Z
F = X'Y'Z + (X+Y)(X+Z')(Y+Z')Z
F = X'Y'Z + (X + XZ'+ XY + YZ')(YZ)
F = X'Y'Z + XYZ + 0 + XYZ + 0
F = X'Y'Z + XYZ

Truth Table
X Y Z F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
c)
Expression for Complement of F which is F'
F' = (X'Y'Z + XYZ)'
F' = (X'Y'Z)'(XYZ)'
F' = (X''+ Y'' + Z')(X' + Y' + Z')
F' = (X + Y + Z')(X'+ Y'+ Z')

complement of F' = F'' which is F
and F = F = X'Y'Z + XYZ
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