Question

Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14) b) F(x,y,z)-П (0,3,6,7) 5. Simplify the following Boolean function , using three- variable maps: a) F(x,y,z) - 2 (0,2,6,7) b) F(A,B,C)-Σ (0,2,3,4,6) c) F(a,b,c)=Σ (0,1,2,3,7) d) F(x,y,z)-Σ (3,5,6,7)

Answer 1

(a) Given F = (x+y^'+z) (x^' + z^') (x + y) F^- = [(x+y^'+z) (x^' + z^') (x + y)]^' = [(x+y^'+z)^' + (x^' + z^')^' + (x + y)^'] [Therefore (AB)^' = A^' + B^'] complement is F^- = x^'yz^' + xz + x^'y^' [Therefore (A + B)^' = A^'B^'] (b) Given F = (AB^' + C)D^' + E F^- = [(AB^' + C)D^' + E]^' = [(AB^' + C)D^']^' E^' [(A + B)^' = A^'B^'] = [(AB^' + C)^' + (D^')^'] E^' = [(AB^')^'. C^' + D] E^' complement is F^- = [(A^' + B)C^' + D] E^' (1) Given F = xy + x^'y^' + y^'z --- > (1) (F^_)^' = [(xy + x^'y^' + y^'z)^-]^' f = [(xy)^' (x^'y^')^' (y^'z)^']^' --- > (2) F = [(x^' + y^') (x + y) (y + z^')]^' = [(x^' + y^')^' + (x + y)^' + (y + z^')] --- > (3) (2)(3) from Equation (2)