BOOLEAN ALGEBRA AND LOGIC GATES

Question 1

What is a logic gate and why is it called a gate?

Answer 1

Electronic circuits which combine digital signals
according to the Boolean algebra.
Logic gates are called gates because they control the flow of information.

Question 2

Describe negative and positive logic

Answer 2

 Positive logic is an electronic representation in which the true state is at a higher voltage.
 Negative logic has the true state at a lower voltage.

Question 3

Draw the gate diagram and truth table for the following gates: NOT, AND, NAND, OR, NOR, XNOR, XOR

Answer 3

*See notes for diagrams and truth tables

Question 4

Describe Boolean algebra and its purpose

Answer 4

It is used to express logic functions algebraically.
It is defined with
 a set of elements (any collection of objects having a
common property.)
 a set of operators,
 a number of unproved axioms or postulates.

Question 5

What are axioms and postulates of Boolean algebra

Answer 5

A set of logical expressions that we accept without proof and upon which we can build a set of useful theorems.
EG 0.0=0 or 1+0=1

Question 6

What is a field

Answer 6

A field is a set of elements, together with two binary operators, each having properties 1 through 5 and both operators combining to give property 6.

Question 7

State the duality property

Answer 7

“Every algebraic expression deducible from the
postulates of Boolean algebra remains valid if the operators and identity elements are interchanged”.

Question 8

How is the dual of an algebraic expression obtained

Answer 8

“Every algebraic expression deducible from the
postulates of Boolean algebra remains valid if the operators and identity elements are interchanged”.

Question 9

List the postulates (2, 3, 4,5) and theorems( 1-6) of Boolean algebra

Answer 9

*See notes

Question 10

Justify theorem 1a, 1b, 2a, 2b, 3, 6a and 6b

Answer 10

*See notes

Question 11

Describe a boolean function

Answer 11

A Boolean function expresses the logical relationship
between binary variables.
 It can be represented in a truth table.
 It can be transformed from an algebraic expression into a circuit diagram.

Question 12

What is the difference between a boolean function and a function in its algebraic format?

Answer 12

There is only one way that a Boolean function can be
represented in a truth table.

However, when the function is in algebraic form, it can be expressed in a variety of ways, all of which have equivalent logic.

Question 13

What is a literal?
How many terms and literals do the following expressions have?
a) x′y′z + x′yz + xy′
b) x′z + xy

Answer 13

A single variable within a term in complemented or uncomplemented form.
a)3 Terms, 8 Literals
b)2 Terms, 4 Literals

Question 14

Do the examples on lecturer slide 34

Answer 14

• See lecturer slide 34

Question 15

How is DeMorgan’s theorem used in finding the complement of a function

Answer 15

DeMorgan’s theorems states that the complement of a function is obtained by interchanging AND and OR
operators and complementing each literal..

Question 16

Illustrate Demorgan’s principle in n variables

Answer 16

*See notes

Question 17

Explain De Morgan’s 1st and 2nd theorem in terns of gates

Answer 17

1st- (x+y)’=x’.y’
Inverting output of an OR gate =inverting the inputs of an AND gate

2nd- (xy)’ = x’+y’
Inverting output of an AND gate= Inverting the inputs of an OR gate