Convert each of the following expressions into sum of products and products of sums: (a) (AB + C)(B + C’D) (b) x’ + x(x + y’)(y + z’)
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2) Convert each of the following expressions into sum of products and products of sums:
(a) (AB + C)(B + C’D)
(b) x’ + x(x + y’)(y + z’)
Step by step
Solved in 3 steps
- Simplify the following logical expressions:Eliminate useless variables and symbols. Afterwards, convert to Chomsky Normal Form. (Start variable S) S -> ABBC | BA A-> abB | aa B -> bB | Aa C -> Cb | aC(3) Express the following functions in sum of minterms and product of maxterms forms. (a) F(X,Y,Z)= (X+YZ)(Z+YX) (b) F(X,Y,Z)= X'+X(X+Y')(Y'Z')
- Simplify B (x, y, z) = X’Z+X’Y+YZc) Giving a two complex numbers a= 10+j3, b= 10 < 60° i) Find the real and imaginary part of a and b in MATLAB Use MATLAB to find a+b, a-b, ab and b/a ii) iii) Determine r, 0 and the complex conjugate.3- Simplify the following equation: f(4, B,C,D) = E(0,3,4,6,10,11,14,15) dm(2,7,8,12) where dm is denoted for don't care.
- (Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.1) Simplify the following Boolean functions, using three variable K-maps. a) F(x, y, z) = Σ(0, 1, 2, 3, 5) b) F(x, y, z) = x'y + yz' + y'z'Question Number Four: Answer each one of the following questions in the space assigned: 1- Simplify each of the following expressions using boolean algebra identities: [4 Marks] a- AB + A( CD + CD') b- ( BC' + A'D) ( AB' + CD') 2- Optimize (simplify) the following boolean function F together with the don't care conditions d in Product-of-sums using k-map: F(A,B.C.D) = IIM (1,3,4,6,9,11)+Ed (0,2,5,8,10,12,14)
- 1. Write a program to calculate sin and cos and determine the forward dif- ferentiation. 2. Do the same, but use central difference. 3. Plot all derivatives and compare with the analytical derivative.Express the following function as a sum of minterms and as a product of max terms: F(A, B,C, D) = B'D + A'D + BDTask 3: Simplifying Boolean functions Simplify the following Boolean expression F (A, B) = (A . B) + A' (A+B) Draw the simplified and the original Boolean expression using EWB and make sure that they are booth equivalent by filling-in the following truth table. B F(A, B) (original) Y (Simplified) A 1 1.