NOT GATE

The output of a NOT gate is the _______________

of its input. If the input is TRUE, then the output is

FALSE, and if the input is FALSE, the output is

_______________. NOT gates can have only

one input and one output. A NOT gate is also

known as an inverter.

It can be written as:

C=NOT A, or C=A, or C=A’

A C

LOGIC GATES

Logic gates are pieces of hardware that have one or more inputs and one ________________. Gates can be

combined in such a way to obtain a desired output out of a combination of possible inputs. Logic gates work

with _______________ numbers, therefore the output must always be either a 1 or a 0.

For an ‘N’ number of inputs, the highest possible combination for a gate is 2N

where 2 stands for binary or the possibility of either ‘1’ or ‘0’ (two options) and where ‘N’ is the number of inputs

TRUTH TABLES

Truth tables are tables which are set to list the possible inputs and find their corresponding outputs. By

looking at a truth table, one is able to know the output of any possible combination of inputs!

The NOT gate, the OR gate and the AND gate are three main types of logic gates.

BOOLEAN EXPRESSIONS

Boolean Expressions are equivalent expressions of the logic state of gates. For example, the Boolean

expression for:

a NOT gate with input A and output C: C = NOT A

an OR gate with inputs A & B and output C: C = A OR B

an AND gate with inputs A & B and output C: C = A AND B

Logic GatesAnd - Not - Or

INPUT (A) OUTPUT (C)

0 1

1 0

NOT

A C

Truth table of a NOT gate

or else

INPUT (A) INPUT (B) OUTPUT (C)

0 0 0

0 1 1

1 0 1

1 1 1

CA

B

CA

B

From the Truth Tables note that for n inputs, there are 2n combinations of inputs.

Therefore, if we have 1 input, there are 21 combinations, ____ combinations.

if we have 2 inputs, there are 22 combinations, 4 combinations.

if we have 4 inputs, there are 24 combinations, ____ combinations.

if we have ___ inputs, there are 26 combinations, 64 combinations.

INPUT (A) INPUT (B) OUTPUT (C)

0 0 0

0 1 0

1 0 0

1 1 1

CA

B

CA

B

OR

Truth table of an OR gate

or else

OR GATE

The output of an OR gate is TRUE if

any input is TRUE, otherwise the

output is FALSE. An OR gate have

two or more inputs and one output.

It can be written as:

C=A OR B, or C=A+B, or C=A | B

Truth table of an AND gate

or else

AND GATE

The output of an AND gate is TRUE ifALL inputs are TRUE, otherwise theoutput is FALSE. An AND gate have twoor more inputs and one output.

It can be written as:

C=A AND B, or C=A.B, or C=A^B

AND

Logic Gates ActivitiesFrom the following three circuits draw the trurth tables and explain what happens when you change the stateof the input

Logic circuits

� A student will be able to enter Sixth Form if he gets an O’ Level pass in Maths, English, Maltese, a Science

subject, and any 2 other subjects. Draw up a logic circuit, using either the AND or OR logic gate to

represent this situation, and give the truth table

� A car manufacturing firm wants to introduce a Seat Belt Alarm. When the engine is on and the Seat belt is

not properly in place an alarm is sounded. Using MMLogic produce a logic circuit.

� A student is given a merit certificate if he gets a pass in all subjects or obtains an overall average of 60 in

his annual exam.

a. Draw a logic circuit that would allow a computer to decide which students should get a merit

certificate.

b. Produce the truth table for this circuit.

Figure 1

Figure 2

Figure 3

Boolean Expressions Activities

a. Simplify the following logic equations by using the rules of Boolean algebra.

1. A • C + A • B • C

2. (A + B) • (B + Ā)

3. A • (Ā + C) + C

b. For each of the previous questions, create a circuit for the Boolean expression

before simplification.

c. For each question, create a circuit for the Boolean expression after simplification.

d. Based on these questions, explain why simplifying Boolean expressions is useful

when designing circuits.

For the following circuits, find the Boolean Expression and construct the truth table

1 2

3

4

5

6

7

8

9 10

Across

3. this expression is always defined in terms on its inputs

4. gate, the output is FALSE if any input is FALSE, otherwise the output is TRUE

5. device is one that can be set to a number of different separate values or states

6. gate, the output is TRUE if any input is TRUE, otherwise the output is FALSE

7. is a notation used in Boolean algebra for defining the output of a logic gate or a logic circuit for

all possible combinations of inputs

Down

1&7. is a hardware item that has one or more input and one output

2. device is one in which data is represented by some quantity which is continuously varying

8. an inverter gate

10. stands for binary digit and is considered as the smallest unit of processing, storage etc.