Minimize the following boolean function- F(A, B, C) = Σm(0, 1, 6, 7) + Σd(3, 4, 5) Fill the cells of the K Map using the given boolean function. Form groups based on k-map rules What is the minimized boolean expression? Provide the minimized truth table. Provide the Logic Gate Circuit
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Minimize the following boolean function-
F(A, B, C) = Σm(0, 1, 6, 7) + Σd(3, 4, 5)
- Fill the cells of the K Map using the given boolean function.
- Form groups based on k-map rules
- What is the minimized boolean expression?
- Provide the minimized truth table.
- Provide the Logic Gate Circuit
Step by step
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- a) Create a 4 Variable Karnaugh Map in paper by mapping 1’s for given standard SOP Boolean expression. After mapping , make relevant groups within Karnaugh Map by considering rules for making groups for 4 variable Karnaugh Map. After making relevant grouping , extract the minimum SOP expression by considering rules for extracting minimum SOP using Karnaugh Map. * Standard SOP: *Create Circuit Diagram using logic gates and logic converter in Multisim for given standard SOP and minimum SOP which you have solved. Do make sure that truth table for both expressions should evaluate same result.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 forms4. A combinational logic circuit that compares between two 2-bit numbers A (AI A0) and B (RI RO) is designed. Output Fis high when A >R and low when AA 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 POSPlease design a 6:1 multiplexer following the below procedures with data inputs of D5, D4, D3,D2, D1, D0 and output of Y.1 How many select signals are needed for this Mux.2) List a truth table for this Mux. Note: for all the unused combinations of select signals, Y=D5Develop an optimized function for this Mux.4Sketch the logic diagram of implementing this 6:1 Mux. Write a complete VHDL structural model to implement the above 6:1 multiplexer. Assume allthe required sub-component (standard gates) VHDL models are given/known that you can use.1. Derive the logical expression of the Full Subtracter Circuit with inputs A,B and C and outputs Diff (Difference) and Br (Borrow). Use K-Map in simplifying the Truth Table outputs expressed as sum of minterms. Required: K Map for Diff K Map for Br Logic Expression for Diff Logic Expression for Br Combined Logic Circuits of Diff and Br1-Using the Karnaugh Method, design and draw the circuit of the logic circuit that gives the result of the multiplication of the two-bit numbers "AB" and "CD" according to minterms (SOP). Do not make any further simplifications before or after the Karnaugh Method. In tables and Karnaugh, ensure that the least significant bit is on the far right and the entries are sorted alphabetically. Make sure that the circuit you have drawn is understandable, the function you have written and the truth table are readable.2. Design a combinational logic circuit for 4-input majority circuit. A majority circuit is one which produces a HIGH (1) output when three or more inputs are HIGH (1). i. Construct the truth table and simplify the Boolean expression into SOP and POS forms using К-mаp. ii. Construct the logic diagram using AND-OR gate network with simplified SOP expression. iii. Construct the logic diagram using OR-AND gate network with simplified POS expression. iv. Construct the logic diagram using only NAND gates with simplified SOP expression. v. Construct the logic diagram using only NOR gates with simplified POS expression.Consider a logic function with three inputs, A, B, and C, and three outputs, D, E, and F. The function is defi ned as follows: D is true if at least one input is true, E is true if exactly two inputs are true, and F is true only if all three inputs are true. Show the truth table for this function.4. A combinational logic circuit that compares between two 2-bit numbers A (AI A0) and B (B1 B0) is designed. Output F is high when A > B and low when A < B. a. Are there any conditions which cause none of the outputs to be asserted? If the conditions exist, what are the inputs? b. Derive the truth table and obtain the maxterm notation for the output. c. Obtain the minimized POS expression of the logic circuit. d. Draw the logic circuit using basic gates.Design a combinational circuit that accepts a 2-bit number (AB) and generates a 5-bit binary number output (S4, S3, S2, S1, So) equal to the cube of the input signals. a) Draw the truth table. Input Output minterm A S4 S3 S2 S1 So b) Derive the Boolean expression of each output signal in POS Form. (product of sum) c) Draw the logic diagram of the circuit. Label all lines.Please design a 6:1 multiplexer following the below procedures with data inputs of D5, D4, D3,D2, D1, D0 and output of Y.1 How many select signals are needed for this Mux.2) List a truth table for this Mux. Note: for all the unused combinations of select signals, Y=D53) Develop an optimized function for this Mux.4) Sketch the logic diagram of implementing this 6:1 Mux.5) Write a complete VHDL structural model to implement the above 6:1 multiplexer. Assume allthe required sub-component (standard gates) VHDL models are given/known that you can useSEE MORE QUESTIONS