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- 5- For the Boolean function: F= XY'Z +X'Y’Z+W'XY+ WX'Y + WXY (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the funetion from the simplified expression and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).Q1. Simplify the following expressions. (a)* xy + xy' (c)* xyz + x'y+xyz' (e) (a+b+c)(a' b' + c) Q2. Develop the truth table of the functions. (a)* F=xy+xy' +y'z Q3. Implement the Boolean function (b) (x + y) (x + y) (d)* (A + B)'(A' + B')' (f) a'bc+abe' + abc + a'be' (b) F=bc+ a'c' F = xy + x'y' + y'z (a) With AND, OR, and inverter gates (b)* With OR and inverter gates (c) (d) With AND and inverter gates With NAND and inverter gates (e) With NOR and inverter gatesQUESTION 9 Give the Boolean expression of F then simplify it: DD-
- ---SIMPLIFICATION VIA BOOLEAN ALGEBRA--- 1.) Use boolean algebra to simplify the equation. SHOW YOUR WORK, one step per line. You should use only variable names, negation (with ``), AND (by putting terms next to each other), OR (with `+`), and parentheses. In addition, each line should start with an equal sign (`=`). The first step has been done for you to show how. As a hint, problem 1c requires De Morgan's Law. Example) f(Z,Y,X) = (!Z+Z)Y!X + !YX = Y!X + !YX = !ZY!X + ZY!X + !YX la) f(A,B,C) = !A!BC + A!B!C + !ABC + !AB!C + A!BCQ6. For the Boolean function F = xy'z + x'y'z + w'xy + wx'y + wxy (a) Obtain the truth table of F (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). (d) (e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).5- For the Boolean function: F= XY'Z+X'Y'Z+W'XY+ WX'Y+ WXY (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).
- Q2: Given the Boolean function F = xy'z + x'y'z + w'xy + wx'y + wxy (a) Obtain the truth table of the function. (b) Draw the logic diagram using the original Boolean expression. (c) Simplify the function to a minimum number of literals using Boolean algebra.The Boolean function ?(?, ?, ?, ?) = ∑ ? (0,5, 7, 8, 9,11). Simplify the function using appropriatelaws and Rules of Boolean AlgebraFor the Boolean function: F = XY'Z+ X'Y’Z+W'XY + WX'Y + WXY Obtain the truth table of F. Draw the logic diagram, using the original Boolean expression. Use Boolean algebra to simplify the function to a minimum number of literals. Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).
- Use refinement to provide a correct implementation of a boolean function checking whether a number is even.2 .A logic operator not defined in this chapter is the NAND function; it is denoted by ↑. NAND is short for “not AND” where a ↑ b ≡ ~ (a ∧ b).a. Give the truth table for the two-input NAND functionb.Show that the NAND operator can be used to simulate each of the AND, OR, and NOT operators. For the first part you need a truth table, but you need to answer the second part of the question correctly too. You need to show what rules you have used to get the conclusion. For that purpose look at the following instructions: In chapter 5, you have learned about De Morgan’s Law. You have also learned how to prove the validity of propositional logic arguments. Please refer to section 5.2.3 of your book to learn more about these concepts. To answer the second part of the questions, you should know well about the above laws and logics and you need to know how and where to apply De Morgan’s Law, implication, conjunction, double negation and so on…. To show that NAND is equivalent to not, you…5- For the Boolean function: F=XY'Z+X'YZ+W'XY+ WX'Y+ WXY (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).