f (v, w, x, y,z) = Σ m(3,7,12,14,15,19,23,25,28,29,31)+ Σ d(4,5,6,9,13)
1. Obtain the most cost efficient function by theoretical procedures
• Use Karnaught maps or/and Boolean algebra to derived the simplified solution.
f (v, w, x, y,z) = Σ m(3,7,12,14,15,19,23,25,28,29,31)+ Σ d(4,5,6,9,13) 1. Obtain the most cost efficient...
I Using K-Map minimize the function: f(x, y, z, w) = {(2, 4, 9, 15) + d(0, 1, 3, 6, 11,13) Do not use Boolean algebra. Use K-Maps.
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)
Q2: 1. Proof this Boolean expression. Use Boolean Algebra (X+Y). (Z+W).(X'+Y+W) = Y.Z+X.W+Y.W 2. For this BF F(X,,Z)=((XYZ)(X +Z))(X+Y) • Design the digital circuit Derive the Boolean Function of X, Y, Z. Simplify the Function Derive the truth table before and after simplification. Derive the BF F(X,Y,Z) as Maxterms (POS) and miterms (SOP). Implement the F(X,Y,Z) after simplification using NAND gates only. Implement the F(X,Y,Z) after simplification using OR NOR gates only.
1. (8 points) Obtain a minimal SOP form for the boolean function f(x,y,z,w) implemented by logic network below. Compare the gate count and number of gate inputs in your minimal SOP expression with those for the network below. f(x,y,z,w)
I would like to know if the SOP function f(v,w,x,y,z)=(x+z)(w+y)(!w+x+!y)(!y+z+!v) and The Quartus II obtained function F(v,w,x,y,z)=(v((!x(z(!w xor (!y))))+(x((!y(w))+(y((z)))))))+(!v((!x(z(!w xor (!y))))+(x(((y))+(w))))) for the above SOP are equivalent?
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)
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).
Q31 For the figure shown below W is an input, (X, Y and Z) are connected to (S2, S and So), find the Boolean function F (W, X, Y, Z) in SOP and implement it use: 1. Multiplexer: One-piece (4 to 1) and external gates (W, X are selectors). 2. Decoder: Five (2 to 4) with AND gate. 0 1 8 to 1 MUX Do D, F OP D, S S S 35 Marks] X Y Z Q31 For the...
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)
I. a) (4 points) For a given function F(x, y, z) = xz + (y + z)(x + z) Draw the logic circuit diagram of the function: b) Using Boolean Algebra to simply the above function c) Use Demorgan's Theorem to find out the complement of the above function F(x,y,z)xz+ + 2)(x +z)