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[VXLTUTORIAL COMPUTER CLASSES BY: VINOD KHARE] PH: 9336061496, , ASSIGNMENT SHEET 3, SOP & POS, Question 1:, Write the Sum of Product (SOP) form of the function F(P, Q, R)for the following, truth table representation of F:, , Question 2:, Write the Product of Sum (POS) form of the function F(X, Y, Z)for the following, truth table representation of F:
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[VXLTUTORIAL COMPUTER CLASSES BY: VINOD KHARE] PH: 9336061496, Question 3:, Represent (P +, , R) in POS form., , Question 4:, Convert the following boolean expression into the equivalent canonical Product, of Sum (POS) form:, A., , .C +, , .B.C +, , .B., , Question 5:, Convert the following boolean expression into its equivalent canonical Sum of, Product (SOP) form:, (, , +v+, , ).(u +, , +, , ).(u + v + w), , Question 6:, State and verify associative laws., Question 7:, Given the following truth table, derive a Sum of Product (SOP) and Product of, Sum (POS) form of boolean expression from it:, , Question 8:, , Question 9:
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[VXLTUTORIAL COMPUTER CLASSES BY: VINOD KHARE] PH: 9336061496, Question 10:, A boolean function F defined on three input variables X, Y and Z is, if and only, if number of 1 input is odd. Draw the truth table for the above function and, express it in canonical SOP form., Question 11:, Write max term expression corresponding to the following truth table:, A, , B, , C, , D (Output), , 0, , 0, , 0, , 0, , 0, , 0, , 1, , 0, , 0, , 1, , 0, , 0, , 0, , 1, , 1, , 1, , 1, , 0, , 0, , 0, , 1, , 0, , 1, , 1, , 1, , 1, , 0, , 1, , 1, , 1, , 1, , 1, , Question 12:, Draw the truth table for the logical function M for three inputs A, B and C,, where M = F (A, B, C). The output is 0 (zero), if the majority of inputs are zero, (0) and one (1) if the majority of inputs are one (1)., Write the sum of products expression (SOP) for M., Question 13:, Express in the product of sum (POS) form, the boolean function F (A, B, C). The, truth table for which is given below:, A, , B, , C, , F, , 0, , 0, , 0, , 0, , 0, , 0, , 1, , 1, , 0, , 1, , 0, , 0, , 0, , 1, , 1, , 1, , 1, , 0, , 0, , 0
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[VXLTUTORIAL COMPUTER CLASSES BY: VINOD KHARE] PH: 9336061496, A, , B, , C, , F, , 1, , 0, , 1, , 1, , 1, , 1, , 0, , 0, , 1, , 1, , 1, , 1, , Question 14:, A combinational logic circuit with three inputs P,Q,R produces 1 if and only if, an odd number of 0's are inputs., 1. Draw a truth table., 2. Derive a canonical SOP expression for the above truth table., 3. Find the complement of the above derived expression using De-Morgan's, theorem and verify whether it is equivalent to its POS expression or not., Question 15:, Given F (X, Y, Z) = (X' + Y').(Y + Z'), Write the function in canonical POS form., Question 16:, If A = 1, B = 0, C = 1 and D = 1, find its, 1. maxterm, 2. minterm, Question 17:, Convert the following cardinal expression into its canonical form and reduce it, using Boolean laws:, F(L, M, O, P) = π(0, 2, 8, 10), Question 18:, What is the application of boolean algebra in computer science?, Question 19:, Convert (X' + Y + Z').(X + Y' + Z).(X + Y + Z').(X + Y + Z) into SOP form., Question 20:, A factory needs a minimum of 1200 tons of raw material and at least 100, workers to start its production. There are three suppliers each agreed to supply, 600, 800 and 1250 tons of raw materials respectively., A=1 if the first supplier supplies else it is 0., B=1 if the second supplier supplies else it is 0.
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[VXLTUTORIAL COMPUTER CLASSES BY: VINOD KHARE] PH: 9336061496, C=1 if the third supplier supplies else it is 0., D=1 if 100 workers are available else it is 0., R=1 if production starts else it is 0., (a) Taking A, B, C and D as inputs and R as output draw truth table for the, problem stated above and derive its SOP expression., (b) Reduce the above SOP expression using the K-map., Question 21:, Given below is the truth table for a combinational circuit for which the input is, a 3 bit number and output is its 2's complement., Inputs, X, Y, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, , Z, 0, 1, 0, 1, 0, 1, 0, 1, , Outputs, P, Q, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, , R, 0, 1, 0, 1, 0, 1, 0, 1, , Write SOP expression for the outputs P, Q and R. Reduce them, if possible,, using the Karnaugh's map., Question 22:, Convert the following function into its canonical sum of product form:, F(X, Y, Z) = Σ(0,1,5,7), Question 23:, Show that dual of P'QR' + PQ'R + P'Q'R is equal to the complement of, PQ'R + Q.(P'R' + PR'), Question 24:, What are maxterms? Convert the following function as a product of maxterms:, F(P, Q, R)= (P + Q).(P' + R'), Question 25:, Simplify the following expression and convert it into its canonical POS form:, (X.Y + Z)(Y + Z'.X), Question 26:, Prove that F(a, b, c) = π(2, 3, 4, 7) = Σ(0, 1, 5, 6).
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[VXLTUTORIAL COMPUTER CLASSES BY: VINOD KHARE] PH: 9336061496, , Question 27:, Design a circuit (3 inputs) which gives a high output only when there is even, number of low or high inputs.
