a) Simplify the following Boolean expressions to a minimum number of literals: a) b) c) d) xy + xy' (x + y)(x + y) xyz + x'y + xyz' (x + y)' (x' + y')' b) Draw two logic diagrams of the circuits that implement the original and simplified expressions in part (a) above.
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- 3. Determine the complement of the following Boolean function [Do not change the form of the given expression]: F(A, B, C, D) = {(B + C')AD} + {D'(A' + C)}(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression s: 2, r'-0. ((r')). r), n -n +½. (b) Given a regular expression 7; = a(ab)* +b°a*, r, = (b + a)* +a*, find L(;) and L(r,), the languages associated with i and r3, respective ly. (c) Find a regular expression r such that L(r) is the same as L = {b"ab",(ba)* : n, m2 0,h2 1}. %3D24 ) There are ABCDE Variables. (5 Variables) In the following cases, logic expression returns 1. A B C D E 1 1 1 1 1 1 1 1 1 1 1 1 1 *Reduce the function ( by using third order MEV method and K-map) And write the logical Expression. And Draw the Circuit.
- Question #1: Given the following logic function: f (a,b,c,d) = E(2,3,8,10,13,15), perform each of the following tasks. 1) Write the logic function fin sum of minterms form using the variables a,b,c, and d 2) Write the logic function fin product of maxterms form using the variables a,b,c, and d 3) Write the complement and the dual of the logic function f(using Eand I7symbols). 4) Using Logisim, draw the logic diagram of the logic function fusing two-level AND-OR gates. By poking the input values in Logisim, construct the truth table of f. 5) Using Logisim, draw the logic diagram of the logic function fusing NAND gates only. By poking the input values in Logisim, construct the truth table of f. 6) Using Logisim, draw the logic diagram of the logic function fusing NOR gates only. By poking the input values in Logisim, construct the truth table of f. Question #2: Given the following logic function: F2(w, x,y, z) = (x+y'z’)(wx'z + w'yz'), perform each of the following tasks. 1) Using…: Simplify the following Boolean expressions to a minimum * :number of literals F = abc + (a + c) + ābcQ2: 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.
- 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).Q1) Simplify the following functions using Boolean algebra • F = A'BC + AB'C' + A'B'C'+ AB'C' + ABC F = ((A + B + C)D)4) Simplify the Boolean expression to a minimum number of literals: a'bc+abc' + abc+a'bc' (4 pts)
- 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).B. Using Algebraic manipulation, simplify the following function. H(A.B,C,D)=( B + C )(A + D ) + D (AC+AB)Using the following variable bindings: (setq x ‘(a b c d)) (setq y ‘(1 2 3 4)) Using only variables x and y, car, cdr, and cons, use Lisp expressions to generate: