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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- QUESTION 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 tableConsider 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…Please compelet only D and E
- 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…Implement the following Boolean function with a 4 x 1 multiplexer and external gates. Connect inputs A and B to the selection lines. The input requirements 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. These functions may have to be implemented with external gates. F(A, B, C, D) = E(1, 3, 4, 10,11, 12, 13, 14, 15) %3D
- 1) What is the biggest binary number (decimal value) you can write with 6 bits? What is the biggest binary number (decimal value and in terms of n) you can write with n bits? If you want to represent the decimal numbers from 0-16, what is the minimum number of bits you will need? Convert the decimal number 238 to binary number. (ZERO point if not showing steps/calculation!)1. Gray code to Binary converter: Gray code is one of the codes used in digital systems. It has the advantage over binary numbers that only one bit in the code word changes when going from one number to the next. (See Table 1). Design a combinational circuit with 4 inputs and 4 outputs that converts a four- bit gray code number into an equivalent four-bit Binary number. Use Karnaugh map technique for simplification. Use LogicWorks for pre-lab demonstrations. Select the library "7400dev.clf* in the Parts Palette and then select the XOR chip 74-86. This would give you a set of 4 XOR's as shown in Fig. 1, just like the hardware chip 74-86. You could use as many as needed from these XOR gates in your design. Get back to ALL LIBRARIES and select switches for the inputs and Binary Probes as indicators of the outputs. Verify your design in the pre-Lab. During the Lab construct the circuit and verify its operations.Use muxes to implement various gates. In each circuit, draw the specified number of 2:1 muxes and implement the given boolean expression. A mux input can be A, B, 0, 1, or the output of another device (e.g., another mux or a decoder). Be sure to label the S, 0, and 1 inputs of every mux. a. Use one 2:1 mux to implement NOT A (i.e. A') b. Use two 2:1 muxes to implement A NAND B c. Use one 2:4 decoder and one 2:1 mux to implement A XOR B Note that the 2-bit values on the right are arranged as B1 B0 (that is, the bottom wire corresponds to the first, not the second, bit).
- Alert dont submit AI generated answer.Course: Computer Engineering Subject: Logic Circuit and Switch Theory Find a function to detect an error in the representation of a decimal digit in BCD. In other words, write an equation with value 1 when the inputs are any one of the six unused bit combinations in the BCD code, and value 0 otherwise. Course: Computer Engineering Subject: Logic Circuit and Switch TheoryPLEASE HELP WITH PARTS A,B,C