Question

In the logical design circuit, DE Morgan’s formulated theories which support the operations of digital design and other operations in the digital world. In your own understanding

(i) Kindly determine three inputs of these theories in its dual form as SOP and POS. (7marks) AP

(b)Design a circuit to determine the relations of the dual theories.

(i) What truth tables’ relationship will your design have?

(ii) Demonstrate graphical representation of input and output signals as a functions of time? (8marks) CR

(c) (C) Simplifier the following Boolean algebra.

(i) (X + Y' + XY) (X + Y') (X'Y) = 0

(ii) ABC + ABC' + AB'C + A'BC = AB + AC + BC

Answer 1

. for imple . Тя Sof во с. Арс 4 dual of this sop's + 0, 4 ) . (к" - 04) (А «Ert) ІІ 115 we take pos fore pie F: A) + ) . Свя ) +с). (A ++) dual form for this pos as (р. 1) - я (п'gO) (Agle")

we re (b) need (1) to get the truth table, to take dual form of sop A B C + A'B' c A AB'C' dual form is + (A + B + 1) . (Al+B'+() (A + B +) truth table for Truth table for to A BO of a 0 o 0 e - 0 1 O 1 1 1 10 V 1 These are not self dual

Example for self dual f(x,y, ) its dual is хутч +1х 4 (1,ч,) (утч) ( v-1) (tt) ху + чап ?, is a self duy оз (х - у - ху) C ++) (4ч) - 6 (~ ~ ' хv) (~~' + 1 x' ) 0 о ABC + ABC + ABC TA BC & AB +BC + AC Ablety By taking RHS, we can prove it LHS A+A } А-1, c + Ac Beal : д% ( ) 4ъс сл+к) Але сь. Асль + (Авс «Лос Ат с дес + дрС + де дос + дъс LHS -RAS