Use Karnaugh maps to simplify the following Boolean functions ex minterms 1. a) fx,y,z)-ml +m2+ m5+m6+...
Simplify the following Boolean functions using four-variable maps: F(w, x, y, z) = Σ (1, 4, 5, 6, 12, 14, 15) F(w, x, y, z) = Π (0, 1, 4, 5, 6, 7, 8, 9) AB’C + B’C’D’ + BCD + ACD’ + A’B’C+ A’BC’D (A xor B)’ (C xor D)
1. (10%) Simplify the following Boolean functions or expression, using three-variable maps (0,2,4, 5,6 F(x, y,) lal 4 bl F(r, y, z)xy x'yz y
4. Express the Boolean functions F as both a sum-of-minterms and a product-of-maxterms 1 0 0 0 Express the following function as a sum-of-minterms F(a, y,z) (zy)' +zy+ Convert the function from the above question into a prodtuct-of macterms Use the K-map to simplify the three variable Boolean functions F(u,x, y, z) = Σ (0, 2, 3, 4, 5, 8, 12, 15) 00 01 11 10 00 10 11 01 1 1 0 0 11 1 0 0 0 10...
Design a PLA that implements the followingthree boolean function A(w,x,y,z) = ?m(4, 5, 7, 12, 13, 15) B(w,x,y,z) = ?m(0, 1, 4, 5, 8, 9, 11, 12, 13, 15) C(w,x,y,z) = ?m(0, 1, 2, 3, 6, 7, 8, 9, 10, 11, 14) a) Use Karnaugh Maps to optimal each function and its complement. b)Select the three optimal functions to use in the PLA. C)Optimize the equation(s) using Karnaugh Map(s). d.Draw the circuit (Don't forget the clock).
Using K-map simplify the following Boolean functions in product of sum form a. F(w,x,y,z) =Σ(0,2,5,6,7,8,10)
Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. F_a = sigma_w, x, y, z(0, 1, 3, 5, 14) + d(8, 15) F_b = sigma_w, x, y, z(0, 1, 2, 8, 11) + d(3, 9, 15) F_c = sigma_A, B, C, D (4, 6, 7, 9, 13) + d(12) F_d = sigma_W, X, Y, Z (4, 5, 9, 13, 15) + d{0, 1, 7, 11, 12)
1. (15 pts) Simplify the following Boolean functions using K-maps: a. F(x,y,z) = (1,4,5,6,7) b. F(x, y, z) = (xy + xyz + xyz c. F(A,B,C,D) = 20,2,4,5,6,7,8,10,13,15) d. F(A,B,C,D) = A'B'C'D' + AB'C + B'CD' + ABCD' + BC'D e. F(A,B,C,D,E) = (0,1,4,5,16,17,21,25,29) 2. (12 pts) Consider the combinational logic circuit below and answer the following: a. Derive the Boolean expressions for Fi and F2 as functions of A, B, C, and D. b. List the complete truth table...
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)...
Using K-maps, obtain the simplified product-of-sums and sum-of-products expressions for the following Boolean functions: a). b). F(x, y,2)-(3,5,6,7) d(0, 1,2) F(w,x, y, z) (0,1,2,3,7,8, 10)+ d(5,6,11, 15)
1. (12 points) Simplify the following Boolean functions using K-maps to get smallest implementation (in terms of number of inverters and 2-input AND, and OR gates used): a. F(a, b,c,d) b + bcd +ac a b. W(m,n, q,r) = n(0,2,8,11,12,13,14,15) D(1,4,6,9,10) c. Z(a, b,c, d)E(1,5,7,9,10,12,13) d(0,8,15)