CSE 1520 Computer Use: Fundamentals - PowerPoint PPT Presentation

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CSE 1520 Computer Use: Fundamentals

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Title: CSE 1520 Computer Use: Fundamentals

1
• Week 6 Gates and Circuits PART I

2
Gates and Circuits
EECS 1520 -- Computer Use Fundamentals
• What is a gate?
• A gate is a device that performs a basic
operation on electrical signals
• What is circuit?
• Gates are combined to form different circuits

3
Gates and Circuits
EECS 1520 -- Computer Use Fundamentals
• Three notational methods to describe the behavior
of gates
• Boolean expressions A form of algebra in which
variables and functions take on only one of two
possible values (0 and 1)
• Logic diagrams graphical representation of a
circuit
• Truth tables defines the function of a gate by
listing all possible input combination and the
corresponding output.

4
Gates and Circuits
EECS 1520 -- Computer Use Fundamentals
• A gate or logic gate performs only one logical
function. Each gate accepts one or more input
values and produces a single output value.
• Six types of logic gates
• NOT
• AND
• OR
• XOR
• NAND
• NOR

5
Gates and Circuits NOT Gate
EECS 1520 -- Computer Use Fundamentals
• Also referred to as an inverter
• If the input value is 1, the output is 0 if the
input value is 0, the output is 1

Logic diagram Symbol
Truth Table
Boolean Expression
• Sometimes the mark is replaced by
horizontal bar placed over the value

6
Gates and Circuits AND Gate
EECS 1520 -- Computer Use Fundamentals
• If the two input values are both 1, the output is
1 otherwise, the output is 0

Logic diagram Symbol
Truth Table
Boolean Expression
• Sometimes the . mark is replaced by the
asterisk symbol

7
Gates and Circuits OR Gate
EECS 1520 -- Computer Use Fundamentals
• If both input values are both 0, the output is 0
otherwise, the output is 1

Logic diagram Symbol
Truth Table
Boolean Expression
8
Gates and Circuits XOR or exclusive OR Gate
EECS 1520 -- Computer Use Fundamentals
• If the two inputs are the same, the output is 0
otherwise, the output is 1

Logic diagram Symbol
Truth Table
Boolean Expression
• Not the difference between the XOR gate and the
OR gate they only differ in one input situation
• When both input signals are 1, OR gate produces a
1 and the XOR gate produces a 0

9
Gates and Circuits NOR Gate
EECS 1520 -- Computer Use Fundamentals
• The NOR gate is essentially the opposite of the
OR gate. That is, the output of a NOR gate is
the same as if you took the output of an OR gate
and put it through a NOT gate

Logic diagram Symbol
Truth Table
Boolean Expression
10
Gates and Circuits NAND Gate
EECS 1520 -- Computer Use Fundamentals
• The NAND gate is the opposite of the AND gate.

Logic diagram Symbol
Truth Table
Boolean Expression
11
Transistors
EECS 1520 -- Computer Use Fundamentals
• How do we implement the gates?
• A gate uses one or more transistors to establish
how the input values map to the output value
• A transistor acts like a switch.
• It either turns on to conduct electricity or
turns off to block the flow of electricity

12
Transistors
EECS 1520 -- Computer Use Fundamentals
• A transistor has three terminals source, base
and emitter

source
output
base
emitter
• When an electrical signal is grounded, it has 0
volts!
• If the source signal is pulled to ground, the
output signal is low output is 0
• If the source signal remains high, the output
signal is high output is 1

13
Transistors NOT Gate
EECS 1520 -- Computer Use Fundamentals
• The output is determined by the base electrical
signal.

source
Vout
Vin Vout
1 0
0 1
base
Vin
emitter
• If Vin is high, the source is pulled to ground
and Vout is low (i.e. 0)
• If Vin is low, the source is not grounded and
Vout is high (i.e. 1)

NOT Gate needs 1 transistor
14
Transistors NAND Gate
EECS 1520 -- Computer Use Fundamentals
source
Vout
Vin1 Vin2 Vout
0 0 1
0 1 1
1 0 1
1 1 0
Vin1
Vin2
emitter
• If Vin1 and Vin2 are high, the source is pulled
to ground and Vout is low (i.e. 0)
• If Vin1 and Vin2 are low, the source is not
grounded and Vout is high (i.e. 1)
• If either Vin1 or Vin2 is low, the source is not
grounded and Vout is high (i.e. 1)

NAND Gate needs 2 transistors
15
Transistors NOR Gate
EECS 1520 -- Computer Use Fundamentals
source
Vin1 Vin2 Vout
0 0 1
0 1 0
1 0 0
1 1 0
Vout
Vin1
Vin2
emitter
emitter
• If Vin1 and Vin2 are high, the source is pulled
to ground and Vout is low (i.e. 0)
• If Vin1 and Vin2 are low, the source is not
grounded and Vout is high (i.e. 1)
• If either Vin1 or Vin2 is low, the source is
grounded and Vout is low (i.e. 0)

NOR Gate needs 2 transistors
16
Transistors OR Gate
EECS 1520 -- Computer Use Fundamentals
• Since OR gate is the opposite of NOR gate, how
many transistors would you think will be required
to implement the OR gate?

OR Gate needs 3 transistors
17
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• Gates are combined into circuits by using the
output of one gate as the input for another gate.
• For example

18
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• For example

Logic diagram Symbol
Truth Table
• Since there are 3 inputs, there are 8 possible
outcomes

19
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• For example

Logic diagram Symbol
Boolean expression
• D A B
• E AC
• X AB AC

20
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• Now, we want to investigate the following Boolean
expression

X A(BC)
• How do we want to create the logic diagram
(called circuit 2) of the above Boolean
expression?

- We have an inner function which consists of an
OR gate between B and C - We then have an
outer function which is an AND gate between
A and (BC)
Logic diagram Symbol (circuit 2)
A(BC)
BC
21
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• We have the following

X A(BC)
Boolean expression
Logic diagram Symbol
A(BC)
BC
A B C BC A(BC)
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
A B C BC A(BC)
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
A B C BC A(BC)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 1 0
1 0 0 0 0
1 0 1 1 1
1 1 0 1 1
1 1 1 1 1
Truth table
22
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• Circuit 1
• Circuit 2

A(BC)
BC
A B C BC A(BC)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 1 0
1 0 0 0 0
1 0 1 1 1
1 1 0 1 1
1 1 1 1 1
A B C D E X
0 0 0 0 0 0
0 0 1 0 0 0
0 1 0 0 0 0
0 1 1 0 0 0
1 0 0 0 0 0
1 0 1 0 1 1
1 1 0 1 0 1
1 1 1 1 1 1
• Their results are identical!

23
Combinational Circuits
EECS 1520 -- Computer Use Fundamentals
• We have therefore demonstrated circuit equivalence
• That is, both circuits produce the same results
for each input combination
• Boolean algebra allows us to apply provable
mathematical principles to help us design logical
circuits
• From the previous example

X AB AC A(BC)
24
Properties of Boolean Algebra
EECS 1520 -- Computer Use Fundamentals
• DeMorgans law, in particular, is very useful in
Boolean algebra.
• For instance, it means that

___ ___ ___
1 NAND gate is equivalent to 2 NOT gates with an
OR gate