Question

1. Find the Boolean expression of the truth table. Then simplify it and convert it into the least amount of logic gates possible. AB Output 100 011 101 2. Find the POS form of the Boolean expressions below. Find the truth table and logic minimization method of it. Show its gate level implementation, and show the same gate level implementation using only NAND gates. A(X,Y,Z)= m(0,2,4,6) B(X,Y,2)={m(0,4,5) 3. Create a J-k Flip Flop using a D-Flip Flop. Show its truth tables, Boolean expression, excitation tables, and logic implementation.

Answer 1

OO - - O-0- ea-o TAIB Toutput) F= ĀB + ĀB TAB we can write this boolean expression from truth table FoĀB + Ā B +ĀB+AB A+A=A FE ĀB +Ā B+ ĀBUAB * A+Ā=1 FaĀ (B+B) +ő (Aro) F=Ā+ B : F = AB che 2. A(XIV,z) = Em (0,21416) = TTM (1,3,5,7) B(x14,2)=51m (0,4,5) = M(1, 2, 3,6,7) Pos form of Boolean expacgsion: A (8,4,2)=3 B(* 19,2)=(x+2)(7).

XOOOO- Truth tables : A(X,,Z)=m(0,2,4,6). B(xiv, z) = I'M (0,4,5) x y z output. Ay z output. 0 0 0 1 OO! 0 Oi! O Oi! 0 100 1 I 100 > OO- - - OOO- 0 O - - - O 0 O C + + I!! 0 A(x,y,z)- xYz+X Y Z + xYz+ x 72. A(X,Y,Z) = F Z+XYZ + PYŽAXYZ. A(X, Y,Z)-yz(x + y) + Y=(x+1) A(X,Y,Z) = YE+YZ = 2(x+y) ACA,Y,Z) = z oldet er som + z he ACX 1V, z)=7. B(x,y,z) - xyz + xyz + уу ? B(X,Y,Z)= XYZ+XYZ+XYZ +XYZ. B(819,2)=Y7 (x+*) + XY (247) B(X,Y,Z) = XY+Y2

X- iz tara, 4,2), z[Doz F(X,Y,Z) = 87.72 F(X,Y,Z) = X5+52 F(x, y, z) = XY+Y2 Boolean capression 3. JK FF »DFF. ps Өон т к. O * - - al 3 1 I X D Flip Flop truth table D Qn Qnts 0. TK ff excitation table An Qnti I k. X O- ao- X - 00- - - * o * , 0. - , , , J=5'm ()+d (113) Krm ()+d (012)

D@@ 1 8181 KED TED D-TH Ý D K