Page 87 - ComputerScience_Class_11

HALF ADDER 1

A A ⊕ B
B

A.B HALF ADDER 2
C.(A ⊕ B) + A.B

A ⊕ B ⊕ C
C

C.(A ⊕ B)

Let’s Revisit

♦ A proposition is a declarative statement that can either be true or false, but not both or any other value.
♦ Well-Formed Formulas (WFF) are the representation of propositional logic in the form of symbols or abbreviations.
♦ The left part (if) of a conditional is called an antecedent and the right part (then) is called a consequent.
♦ Converse is the proposition obtained by interchanging the antecedent and consequent.
♦ Inverse is the proposition obtained by taking the negated antecedent and the negated consequent in a conditional.
♦ Contrapositive is the proposition that is inverse of its converse.
♦ A tautology is a proposition that has 1 as its truth value and a contradiction has 0 as its truth value.
♦ A contingency has both 0 and 1 as its truth values.

♦ A logic gate is a digital circuit that depicts a logical relationship between the input and output voltages of the circuit. They are
the building blocks of a digital circuit.
♦ The AND gate produces 1 as output when all its inputs are 1.
♦ The OR gate produces 1 as output when any one of its inputs is 1.

♦ The NOT gate inverts the output.
♦ The NAND and NOR gates are called universal gates as they can be used to implement operations of AND or and NOT gates.
♦ The XOR gate produces 1 for odd combinations of 1 and 0 in other cases.
♦ The XNOR gate produces 0 for odd combinations of 1 and 1 for even combinations of 1 or all 0’s.
♦ The half adder is a combinational circuit that is designed to perform the addition of two bits and produce the two binary
outputs as sum (S) and carry(C) bits.
♦ The full adder is a combinational circuit that is designed to perform the addition of three bits and produce the two binary
outputs as sum (S) and carry(C) bits.

Propositional Logic, Hardware Implementation, Arithmetic Operations 85