Construct a karnaugh map for the logic function below with four inputs A, B, C, D, and output E. Then find the minimum sop and minimum POS expressions for E. E=Σm(2,3,4,5,6,7, 11, 15)
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- 1. Given the Boolean expression (b + d)(a’+ b’ + c),a. Convert the expression to the other standard form. What do you call this standard form?b. Derive its canonical form. What do you call this canonical form?c. Derive the other canonical form. What do you call this canonical form?d. Provide the truth table of the expressione. Draw the logic circuit diagrams of the 2 standard formsBoolean Function F(A,B,C,D) = { m (1,2,5,8,11,15), don't cares d(A,B,C,D) = { m (3,10) a. Using a K-map simply F in S.O.P. form b. Draw the logic circuit c. Using a K-map simply F in P.O.S. form d. Draw the logic circuit e. Which form has a lower gate input cost?Design circuit that has an input w and an output z. The circuit is a sequence detector that produces z = 1 when the previous two values of w were 00 or 11; otherwise z = 0. Use W=0101100010101110101011100010 a) For this problem design the circuit using JK flipflops, draw the state diagram, true table, logic circuit.
- Simplify the expression f (A,B,C,D) = Sm (0,1,4,8,9,12,14,15) using K– map and realize the final expression using basic logic.Consider the multiplexer based logic circuit shown in the figure. W Do 0 MUX AF = W S₁ S₂ S₁ B F = WS₁ + WS2 + S1S2 Which one of the following Boolean functions is realized by the circuit? C F=W + S₁ + S₂ 0 DF=W S1 S₂ MUX S₂ FWe need a logic circuit that gives a high output if a given hexadecimal digit is 4, 6, C, or E. The inputs to the logic circuit are the bits B 8, B 4, B 2 and B 1 of the binary equivalent for the hexadecimal digit. (The MSB is B 8 and the LSB is B 1 ) .Construct the Karnaugh map and write the minimized SOP and POS expressions for X.
- Design a circuit that takes the numbers 0 through 7 as inputs (0=000 , 1= 001, 2=010, ...., 7=111)and produces an output of 1 if and only if the input is an even numbera. Draw the truth tableb. Write the functionc. Simplify the function by k-mapd. Draw the logic gates of the simplified functionA majority gate is a digital circuit whose output is 1 only if the majority of inputs are 1 otherwise the output is 0 for all other cases. Design a combinational logic circuit for 4-input majority gate. a. Construct the Truth table. b. Minimize POS Expression using K MAP c. Draw the combinational circuit for minimize POSA B 2. Write the expression for the output Z (in terms of inputs A and B) for the following logic circuit: BPL Z= Z
- A logic circuit has inputs A, B, and C. The output of the circuit is given by D=∏M( 1, 3, 4, 6 ) a. Construct the Karnaugh map for D. b. Find the minimum SOP expression. c. Find the minimum POS expression.a) Using an SR latch and logic gates, design an SN-flipflop which has two input lines (S and N) and two output lines (Q and Q'). The SN-flipflop operates according to the following characteristics table. Determine the characteristics equations and draw circuit diagram of SN-flipflop. Inputs Outputs Q(t+1) Q'(t+1) Q’(t) Q(t) Q(t) Q’(t) Operation S Toggle No-Change 1 1 1 Set 1 1 Q'(t) Q(t) ToggleSimplify the following Boolean expressions using Karnaugh Map and draw the logic circuits. f = wxyz + wxyz + wxyż + wxỹz + wxyz + wxyz + wxỹz + wãyz