Lecturer: Norah Alsufyan

Basics of Logic gates -

Part 1

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 Chapter Outline

• Brief of Digital circuits

• The Meaning of Logic Gates
• How Logic Gates Are Relevant to Computers
• Representation of Gates
1.Logic diagrams
2.Truth tables
3.Boolean expressions
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 Chapter Outline
• Types of Gates
– Three Basic Gate Functions
1. NOT
2. AND
3. OR
– Additional Gate Functions
1. NAND
2. NOR
3. XOR
4. XNOR
• Gates with More Inputs
• Formula to Determine the numbers of possible inputs
• Universal Gates
1. NAND
2. NOR
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• Conclusion
BRIEF OF DIGITAL CIRCUITS

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 Digital circuits

• Digital circuits requires only two voltage

level 0v and 5v.
– Zero volts (0v) represent logic “0”
– Five volts (5v) represent logic “1”

ON (1): connected to power.

OFF (0): not connected to power

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THE MEANING OF LOGIC GATES

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 The Meaning of Logic Gates

• A gate is a device that performs a basic

operation on electrical signals.
• Gates are combined into circuits to perform
more complicated tasks.
• Logic gates are the circuits that are designed
to performed these basic logic functions.
• Actually the term logic is applied to digital
circuits used to implement logic functions.
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 The Meaning of Logic Gates

In other words, logic gates are the circuits that

take one or more inputs signals and send out a
single output signal.
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 The Meaning of Logic Gates

• In this logic gate, there are only two state which

are one is ON State(1) and another is OFF
State(0).
• ON State can be say High input and High output
and OFF State can be say Low input and Low
output.
• ON State means current is passing through the
logic circuit and OFF State means current is not
passing through the logic circuit.
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 The Meaning of Logic Gates

• Several kinds of digital logic circuits are the

basic elements that form the building blocks for
such complex digital system as the computer.
• The lines connected to each symbols are the
inputs and outputs.
• The inputs are on the left of each symbol and
the output is on the right.
• To conclude , A circuit that performs a specific
logic operation (AND, OR, Not, NOR,NAND,
XOR,NXOR) is called a logic gate. 11
HOW LOGIC GATES ARE
RELEVANT TO COMPUTERS

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 Why are these logic gates relevant to computers and
computers technology ?

• Because all computers are ultimately made

out of logic gates.
• Hundreds of millions of various logic gates ,
when working together which makes
computers function as they do.

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REPRESENTATION OF GATES
1. Logic diagrams
2. Truth tables
3. Boolean expressions
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 Representation of Gates

• There are three different, but equally

powerful, notational methods
for describing the behavior of gates
and circuits
– Logic diagrams
– Truth tables
– Boolean expressions

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 1- Logic diagram

• Logic diagram: a graphical representation

of a circuit
– Each type of gate is represented by a specific
graphical symbol

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 2- Truth table

• Truth table: defines the function of a gate

by listing all possible input combinations
that the gate could encounter, and the
corresponding output

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 3- Boolean algebra

• Boolean algebra: expressions in this

algebraic notation are an elegant and
powerful way to demonstrate the activity of
electrical circuits
 AND is denoted by a dot (.)
OR is denoted by a plus (+).
NOT is denoted by a single quote mark (')
after the variable or an overbar ( ¯ ).
XOR is denoted by
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 Note
The statement:
1 + 1 = 2 (read “one plus one equals two”) is
not the same as 1 + 1 = 1 (read “1 or 1
equals 1”).
1.1 = 1 ( read 1 AND 1 equals 1 )

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ACTIVITY #1 - GROUP WORK

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TYPES OF GATES

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 Types of Gates

• Let’s examine the processing of the following

seven types of gates
– NOT
– AND Three Basic Gate Functions
– OR
– XOR
– NAND
Additional Gate Functions
– NOR
– XNOR

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 Types of Gates

 Three Basic Gate Functions

 Using these three gates we can design any
logic circuit.
 Additional Gate Functions
 We will define four additional gates which aid
circuit design.

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THREE BASIC GATE FUNCTIONS
1. NOT
2. AND
3. OR
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 NOT Gate Representation

• A NOT gate accepts one input value

and produces one output value

Figure 4.1 Various representations of a NOT gate

To illustrate how it works visually .. Check this link: https://logic.ly/lessons/

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 What NOT Gate Means

• By definition, if the input value for a NOT

gate is 0, the output value is 1, and if the
input value is 1, the output is 0
• A NOT gate is sometimes referred to as
an inverter because it inverts the input
value

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 Example of NOT Gate

e.g. I turn on the heating if it is NOT hot

if A = hot and Y = Heating on then:

YA
where the bar represents logical NOT.

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Practical Application of “Not”
Logic Gate

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 AND Gate Representation

• An AND gate accepts two input signals

• If the two input values for an AND gate are
both 1, the output is 1; otherwise, the output
is 0

Figure 4.2 Various representations of an AND gate

To illustrate how it works visually .. Check this link: https://logic.ly/lessons/29

 Example of AND gate
e.g. I get up early if I have lectures AND it is a weekday

he said if A = lecture B = weekday and Y = get up early

then he said you can write:

Y  A B
where the dot represents logical AND.

Thus ,
If 1 represents TRUE and 0 represents FALSE
then the function can be defined in a truth table.
Logic Gates 30
How AND Gate Work

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Practical Application of “AND”
Logic Gate

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 OR Gate Representation

• If the two input values are both 0, the

output value is 0; otherwise, the output is 1

Figure 4.3 Various representations of a OR gate

To illustrate how it works visually .. Check this link: https://logic.ly/lessons/33

How OR Gate Work

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 Example of OR Gate

e.g. I turn on my headlights if it is dark OR it is raining

if A = dark B = raining and Y = headlights on then:

Y  A B
where the + sign represents logical OR.

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Practical Application of “OR”
Logic Gate

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ACTIVITY #2 - GROUP WORK

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LAB # 1 - GROUP WORK

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ADDITIONAL GATES FUNCTIONS
1. XOR
2. NAND
3. NOR
4. XNOR 39
 What XOR Gate Means

• XOR, or exclusive OR, gate

– An XOR gate produces 0 if its two inputs are
the same, and a 1 otherwise
– Note the difference between the XOR gate
and the OR gate; they differ only in one
input situation
 When both input signals are 1, the OR gate
produces a 1 and the XOR produces a 0

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 XOR Gate Representation

Figure 4.4 Various representations of an XOR gate

To illustrate how it works visually .. Check this link: https://logic.ly/lessons/41

 NAND and NOR Gates

• The NAND and NOR gates are essentially the

opposite of the AND and OR gates, respectively

Figure 4.5 Various representations

of a NAND gate

Figure 4.6 Various representations

of a NOR gate

To illustrate how it works visually .. Check this link: https://logic.ly/lessons/42

How NAND Gate Work

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How NOR Gate Work

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 XNOR

The XNOR gate is essentially the opposite of the XOR.

To illustrate how it works visually .. Check this link: https://logic.ly/lessons/45

GATES WITH MORE INPUTS

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 Gates with More Inputs

• Gates can be designed to accept three or more

input values
• A three-input AND gate, for example, produces
an output of 1 only if all input values are 1

Figure 4.7 Various representations of a three-input AND gate

To illustrate how it works visually .. Check this link: https://logic.ly/demo/47

How NAND Gate Work With
Two Input

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ACTIVITY #3 - GROUP WORK

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LAB # 3 - GROUP WORK

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 Explain Why there are different in the
numbers of truth table rows =)

• The truth table of NOT have two rows

(0,1)
• The truth table of AND , OR , NOR, XOR,
XNOR with two input have four rows
(00,10,01,11)
• The truth table of AND , OR , NOR, XOR,
XNOR with three input have eight rows
(000,001,010,011,100,101,110,111)
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 Formula to Determine the
numbers of possible inputs
• To determine the total number of possible
combination of binary inputs to a gate is
determined by the following formula: N=2n
 Where N is the number of possible input
combinations and n is the number of input
variables.

• Example,
Two inputs variables; N=22 = 4 Combinations.
Three inputs variables; N=23 = 8 Combinations.
Four inputs variables; N=24 = 16 Combinations.
UNIVERSAL GATES
1- NAND
2- NOR

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 What Universal Gates Means

• NAND and NOR gates are referred to as

universal gates as the three basic gates can be
constructed using either one of the two.
• This therefore implies that all logic circuits can
be constructed using either of the gates.
• The notes show this process for NAND only but
it can be shown for NOR also.

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 NOT Using NANDs Only
• The Truth Table is for a NAND gate
A B Y • If we tie the inputs of a NAND together
0 0 1 then we limit the possible input
0 1 1 combinations to two, 1 1 and 0 0.
1 0 1 • These are shown on the table now if
1 1 0 the input is 0 the output is 1 and vice
versa

a NOT gate

A
Y

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 AND Using NANDs Only

• As a NAND is simply an AND followed by a NOT

gate (inverter) we can simply use a NAND
followed by NOT.
A

Note – more than one NAND gate to

produce the desired AND gate.

Logic Gates 56
 OR Using NANDs Only – Step 1

A B A B
0 0 0
0 1 1
1 0 1
1 1 1

This is our desired OR gate

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 OR Using NANDs Only – Step 2

A B A B A B
0 0 0 1 1
0 1 1 1 0
1 0 1 0 1
1 1 1 0 0

If we now add NOT A and NOT B into our table

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 OR Using NANDs Only – Step 3

A B A B A B A B
0 0 0 1 1 1
0 1 1 1 0 0
1 0 1 0 1 0
1 1 1 0 0 0

If these are now ANDed together

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 OR Using NANDs Only – Step 4

A B A B A B A B A B
0 0 0 1 1 1 0
0 1 1 1 0 0 1
1 0 1 0 1 0 1
1 1 1 0 0 0 1

Finally if we invert our result we see that the

3rd and 7th column are identical. This means that
if we invert the inputs then NAND then we will
end up with the OR function. 60
 OR Using NANDs– in Logic
Diagram Representation

Y
B

Prove that in your notebook =)

Logic Gates 61
Basic Gate Using NANDs

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Basic Gate Using Nors

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 Note

• Conversions from AND, OR, NOT to NAND only

rarely produce a less complex circuit but
normally the complexity is similar.
• The advantage lies in the fact that NAND chips
are readily available and are inexpensive due to
the number sold and that any gates left over can
be used in other circuits as all circuits use the
same gate types.

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ACTIVITY #4 - GROUP WORK

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 Conclusion

• Logic Gate is an electronic circuit which

receive one or more than one input and deliver
single output.
• There are seven logic gates. NOT , OR , AND
are the basic logic gates. NOR , NAND, XOR ,
NXOR are the additional logic gates.
• A NOT gate inverts its single input value.
• An AND gate produces 1 if both input values
are 1.
• An OR gate produces 1 if one or the other or
both input values are 1. 66
 Conclusion

• An XOR gate produces 1 if one or the other

(but not both) input values are 1.
• A NAND gate produces the opposite results
of an AND gate.
• A NOR gate produces the opposite results of
an OR gate.
• A XNOR gate produces the opposite results
of an XOR gate.
• NAND and NOR gates are referred to as
universal gates as the three basic gates can
be constructed using either one of the two. 67
Conclusion

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Conclusion

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