Logical Operations

Question 1

Define and draw OR

Answer 1

Outputs 1 if either input is true

=)>—

Question 2

Define and draw AND

Answer 2

Outputs 1 if both are true
__
=|__ )—

Question 3

Define and draw NOT

Answer 3

Takes the input and outputs it’s opposite

—|>o—

Question 4

Define and draw XOR

Answer 4

Outputs 1 if only one output is true

=))>—

Question 5

Order of precedence

Answer 5

Brackets
NOT
XOR
AND
OR

Question 6

Annulment law
A.0=
A+1=

Answer 6

A.0=0
A+1=1

Question 7

Identity Law
A+0=
A.1=

Answer 7

A+0 =A
A.1=A

Question 8

Idempotent law
A+A=
A.A=

Answer 8

A+A=A
A.A=A

Question 9

Complement law
A.Ā=
A+Ā=

Answer 9

A.Ā=0
A+Ā=1

Question 10

Commutative law
A.B=
A+B=
A⊕B=

Answer 10

A.B=B.A
A+B=B+A
A⊕B=B⊕A

Question 11

Double complement law
𝐴̿=

Answer 11

𝐴̿=A

Question 12

Distributive law
A(B+C)=
A+(B.C)=

Answer 12

A(B+C)=A.B+A.C
A+(B.C)=(A+B).(A+C)

Question 13

Absorptive law
A+(A.B)=
A.(A+B)=

Answer 13

A+(A.B)=A
A(A+B)=A

Question 14

Associative law
A+(B+C)=
A(B.C)=
A⊕(B⊕C)=

Answer 14

A+(B+C)=(A+B)+C
A(B.C)=(A.B)C
A⊕(B⊕C)=(A⊕B)⊕C