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A:0. Worksheet IV-.. Worksheet IV 2021 1. Identify each of the following expressions as SOP, standard SOP, POS, or standard POS: (a) AB + ABD + ĀCD (c) ABC + ABC (b) (A + B + C)(A + B + C) (d) A(A + C)(A + B) 2. Convert each SOP expression in Question 1 to standard form. 3. Convert each POS expression in Question 1 to standard form. 4. Obtain the truth table of the following functions, and express each function in sum-of-minterms and product-of-maxterms form: (a (xy + 2)(y + x) (c) x'z + wx'y + wy:' + w'y' (b) (x +y')(y' + z) (d) (xy + yz' + x'z)(x + z) .5. Simplify the following Boolean expressions to a minimum number of literals: (a) ABC + A'B + ABC' (c) (x + y)'(x' + y') (e) (BC' + A'D)(AB' + CD') (b) x'yz + xz (d) xy + x(wz + wz') (f) (x + y' + z')(x' + z') 6. Write the Boolean equations and draw the logic diagram of the circuit whose outputs are defined by the following truth table: 1 1 1 Page 1 of 1

1. Consider the function of 3 variables specified with the following sum of products (SOP) form. F(X, Y, Z) = XY'Z'+ X'Y a) Specify the function with a canonical SOP form. Use minterm numbers. Minterm numbers can be identified using product terms presented with "0-1-dash" notation. b) Specify the function with a canonical product of sums (POS) from. Use Maxterm numbers. c) Minimize the function using K-map: obtain the minimal SOP and POS forms for the function.

5. In LQR controller technique increasing value of the element 921 in Q matrix can_ a. Increase rise time b. Decreae rise time c. Increase settling time d. Decrease settling time None of all above 6. Positive value of second derivative of control function yields: a. Maximum solution of the control problem b. Minimum solution of the control problem c. Optimum soultion of the control problem d. None of all above

Karnaugh Maps 155 5.21 Simplify the following expression first by using a niap and then by using Boolean alecbra. Use the nap as a guide to determine which theorenis to apply to which terms for the algebraic simplification. F = a'b'c' + a'c'd + bcd + abc + ab' 5.22 Find all prime implicants and all mininum sum-of-products expressions for each of the following functions. (a) (A,B.C.D) = E m(4, 11, 12, 13, 14) + E d(5,6,7,8,9, 10) (b) f(A,B,C,D) = L m(3, 11, 12, 13, 14) + E d(5,6,7,8,9. 10) (c) f(A,B.C,D) = £ m(1, 2, 4, 13, 14) + £ d(5, 6, 7,8,9, 10) (d) (A,B,C.D) = £ m(4, 15) + d(5,6, 7, 8,9, 10) (e) f(A,B,C,D) = L m(3,4, 11, 15) + £ d(5,6,7,8,9, 10) () f(A,B,C,D) = I m(4) +E d(5,6,7,8, 9, 10, 11, 12, 13, 14) (g) fA,B,CD) = £ m(4, 15) + £ d(0, 1, 2,5, 6, 7, 8,9, 10) 5.23 For each function in Problem 5.22, find all minimum product-of-sums expressions. 5.24 Find the minimum sum-of-products expression for (a) E m(0,2, 3,5,6, 7, 11, 12, 13) ( 6) Σm(2,4,8) +Σ d(0,3, 7) ( c ) Σm(1,5, 6,7, 13…

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Information theory course

Let E be the Boolean expression given in the Karnaugh Map in the image below zt ху xy' x'y x'y write E in the form of the complete number of products!

Please note that they are single question. Please do not write this website allow us to answer one part only. This is not true because tutor answer the whole question. I will highly appreciate your effort and give you upvote. Thanks!

1:22 Homework2 S24_64688b88db19e... 3. Implement the following equation on a PLD structure: F = AB+BC + AC Done 4. Use Karnaugh maps to simplify the following Boolean functions expressed in the sum of minterms. Please clearly show your Karnaugh maps, circling, and place your final Boolean equation on the line provided. a. 3 Variables: A(x,y,z) = m0+ m4+m5+m7 b. 3 Variables: B(x,y,z) = m1 + m2 + m4 + m6 c. 4 Variables: C(w, x, y, z) = (0, 2, 4, 5, 7, 8, 10, 13, 14) d. 4 Variables: D(w, x, y, z) = (0, 1, 5, 6, 8, 9, 10, 12, 13, 14) Q

2) Design a 2-to-1 multiplexer in which the inputs and outputs consist of single bits. Provide the truth table for this multiplexer using IN0 and IN1 for the two inputs, S for the select line and OUT for the output correctly. Obtain the minimal standard sum-of-products expression for the output correctly. PS: Please answer Number 3 from or after number 2 3) Obtain the schematic diagram for the mux designed in 2). Use proper conventions as to the labelling of part numbers, instance numbers and pin numbers correctly.

ab'd' + abc + a'bd + a'b'c' + b'c'd' + a'c'd + bcd + acd' Of the 8 terms in the expression above, how many of them are redundant? (Enter a single numerical digit.)

Question 2 Construct a sequence from your Student ID as discussed below? Example: Assume your Student ID is 437818854, and then use the fourth digit from left then the fifth digit as origin (location zero) then use the other four digit are the rest digit numbered in the sequence , as a sequence x[n] as follow [4,3,7,8,1,8,8,5,4] 1. Find the sequence y, = x[3n] 2. Find the sequence y, = x[2n] – u[n – 2] 3. Find the sequence y3 = x[n/2] * u[1 – n] 4. Find the sequence y4 = x[n – 1] * 8[n – 3] 5. Find the sequence ys = x[2n – 3] 6. Find the sequence y, = x[n+ 3]

Create the Kmap and then simplify for the functions (leave in sum-of-products form): F(w, x, y, z) = w′x′y′z + w′x′yz′ + w′xy′z + w′xyz + w′xyz′ + wxy′z + wxyz + wx′y′z

2) Design a 2-to-1 multiplexer in which the inputs and outputs consist of single bits. Provide the truth table for this multiplexer using IN0 and IN1 for the two inputs, S for the select line and OUT for the output correctly. Obtain the minimal standard sum-of-products expression for the output correctly. PS: Number 2 will be used to help answer number 3 3) Obtain the schematic diagram for the mux designed in 2). Use proper conventions as to the labelling of part numbers, instance numbers and pin numbers correctly.