Question

Obtain the combinational circuit diagram of the following

1. ((p ∨ q) ↔ r) ↔ p

2. (¬q ∧ ¬r) ↔ (p → (q ∨ r))

Answer 1

The given equation represents the mathematical logic table.

Meaning of symbols

v - Logical Disjunction (Logical OR)

The statement (p v q) is true if both inuput p & q are true otherwise false.

$\wedge$ - Conjuction (Logical AND)

The statement (p $\wedge$ q) is true if one of the input is true otherwise false.

$\Leftrightarrow$ - Double Implication/ Equivalence (Logical Ex-NOR)

The statement only if both p & q are false or both p & q are tue

$\rightarrow$ - Domain or codomain of function

_ Negation

The statement is true of input p or q is false

From the given statement and by the truth tables of logic gates let us draw the combinational circuits

1. Combinational Circuit

Pvq P (Pra)<> q PDan Pemasarjana Y (Pvq)<>r)<> P.

2.

To implement the logical circuit for this part lets study first the logical expression for p -> q this will be helpful to draw the logical circuit for the expression of part (2)

Combinational Circuit