Show this to be true that any boolean function of four variables can be implemented by using one 4-to-1 multiplexer,one 2-to-4 decoder, and an unlimited number of OR gates (but the fewest number possible). Demonstrate through the example of f (a, b, c, d) = a ̄b ̄d + bc ̄d + b ̄cd + ̄acd.
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- 3- A-) Implement the Boolean function (F) with a 4 X1 multiplexer and two-input-NOR gates. Connect inputs A and B to the selection lines. The input requirement for the four data lines will be a function of variables C and D. These values are obtained by expressing F as a function of C and D for each of the four cases when AB = 00, 01 ,10 and 11. B-) Implement the Boolean function with a 8 X 1 multiplexer. Connect inputs A,B and C to selection lines. F(A, B, С, D) - 2 (1, 3, 5, 9, 10, 14, 15) А So В S1 4 x 1 MUX 1 Y F 2 3QUESTION 1 Which Boolean algebra property allows us to group operands in expression in any order without affecting the results of the operation (e.g. A+B=B+A)? a. associative O b. Distributive C. commutative O d. Boolean QUESTION 2 The systematic reduction (simplification) of logic circuits is accomplished by: a. symbolic reduction b. using Boolean algebra c. TTL logic O d. using a truth tablewrite a boolean expression then simplify
- Consider F(A,B,C) = AB'C + B'C' + A'BC + A'C' 1. Determine how many logic gate inputs would be needed before any simplification. Do not count inputs to NOT gates 2. Use Boolean algebra rules to get the most simplified expression of F(A,B,C). Then determine how many logic gate inputs would be needed after simplification. Again, do not count inputs to NOT gates. 3. Expand the original expression into its canonical SOP representation. 4. Fill out the K-map below using the SOP canonical representation. Group the 1-cells according to the K-map simplification rules. Translate each group into its product term, OR these product terms together, and verify that the expression you get matches the one in Step 2. 5. Draw two circuits in CircuitVerse, one from the original expression for F(A,B,C), the other from the simplified expression in Step 2 or Step 4. Connect the inputs to both circuits, but separate their outputs. Verify through simulation that these two circuits are indeed equivalent. Take…5) below is the accuracy table showing the output values for two separate binary number entries (W and Y) with a length of two bits. Get the simplest form of output functions with the Karnaugh diagram. Draw a logic diagram of the circuit that performs the function of these functions.Describe in detail which functions a, b and C perform for 2-bit binary numbers in the input.A2. Using Boolean algebra, reduce the output equation of the function in Table 1. (You can use the “Karnaugh Map of Table 2" to simplify the logic function obtained). CD AB Table 2 00|01|11| 10 00 01 11 A3. Construct the simplified expression obtained in A2 by only NOR gates. Design and draw the NOR gate 10 connection diagram of the simplified function using only one 4001 IC. using
- PLEASE ANSWER ALL OF THIS QUESTION ASAP!!!a.) Write the boolean algebraic equation for Q in terms of A and B. b.) Simplify the equation using boolean algebra. c.) Create a four state truth table for Q in terms of A and B. d.) Which gate does the diagram represent.Describe the function of a decoder circuit. identify the types and quantity of gates needed to implement a 3-to-8 decoder; either create (or give the location in the text) of a logic diagram of a decoder circuit A decoder is a circuit that changes a input code into a set of signals. It is just the reverse process of encoding, A common type of decoder is a binary decoder, which is a combinational logic circuit that converts binary information from the n coded inputs to a maximum of 2n unique outputs. It takes a binary input, usually in a coded form, and produces a one-bit output, on each of a number of output lines. The logic state (1 or 0) on any of the output lines depends on a particular code appearing on the input lines. Binary decoders are used in a wide variety of applications, including data demultiplexing, seven segment displays, and memory address decoding. If we want to buy a 1 of 8 decoder/ demultiplexer, please give the…