a) Realise the following Boolean expression using 2-INPUT NAND gates only (Show the three steps of implementation). F = X + Y(X + Z) +YZ + (XY + Z)
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- Questions Q1) Why do NAND & NOR Gates called Universal Gates? Q2) Implement Ex-OR & Ex-NOR Gates using: a) NAND Gate only b) NOR Gate only Q3) Apply Demorgan's theorem and Boolean rules to simplify and draw the output of the following expression: Z= (AB(C+BD)+AB)C3- 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 3Logic Gates:* 7404LS (NOT)* 7408LS (AND)* 7432LS (OR)* 7400LS (NAND)* 7402LS (NOR)* 7486LS (EX-OR)Or you can use 74HCxx versions. Task 2: 4 INPUT PRIORITY ENCODERa) Write the truth table.b) Find the outputs in terms of min terms using minimal expression.c) By using K map, find the simple/simplest expression of theoutputs.d) Draw the circuit diagram. (Simulation design will be accepted.)e) Simulate the circuit & explain your results. (Please do notdesign separate simulations for each output. You should design ONEsimulation including all inputs and outputs.)
- A logic function is expressed by the equation = 0.1.8.9.4. Plot the the values on the K-map below Note: w is the msb (most significant bit) 3 x 10 0- - W X 1 00 01 Write the simplified Sum of Products (SOP) expression. Use yz WIM or "" for NOT; 11 10 for AND; "+" for OR (without the quotation marks.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).Draw the equivalent logic circuit diagram of the following expressions : a. XY = F b. X + Y = F XÝZ = F c. d. XY + XZ = F e. XYZ + XÝZ = F
- 3. Logic Design a. Create the truth table of a 3-input AND gate. Realize the 3-input AND operation using only 2-input NOR gates. b. Create the truth table of a 3-input OR gate. Realize the 3-input OR operation using only 2- input NAND gates. c. Using AND and OR logic gates, implement the logic function: F(x, y, z) = xy + yz + zx d. Using NAND logic gates, implement the logic function: F(x, y, z) = xy + yz + zxB) Simplify the following Boolean expression, then implement by using NOR gates only. [AB(C+ BD) + ABJC1. a. i. Draw the gates required to build a half adder are ii. When simplified with Boolean Algebra (x + y)(x + z) simplifies to : iii. The output of a logic gate is 1 when all its inputs are at logic 0, the gate is either :
- 2- Experiment the boolean expression by using K-Map then draw by using logic gates ( NAND & NOR gates only) Y=A'B'C'D'+A'BC'D+ABCD+AB'CD+A' B'CD'+ABCD'+AB'CD'Implement the function f(x₁₁x₂₁x²₁x₁4₁x₁) = x₁x₂x₂x² + x₁x²₂ + x₁ x3 + x₁x² + x3 x4 x5 by using a 4-to-1 multiplexer and as few other gates Assume that only 3. possible. uncomplemented x,variables are available. asIH.W: Draw a logic eircuit of the following Boolean expression before and after simplification using karnough map and Boolean expression. Y-AB+ AB A B Y 1 1