Chapter 4-Gates and Circuits 4.1 Computers and Electricity A ...

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Nov 27, 2013 (3 years and 7 months ago)

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Chapter 4
-
Gates and Circuits


4.1 Computers and Electricity



A voltage level in the range of 0 to 2 volts is considered “low”

o

Interpreted as binary 0



A voltage level in the range of 2 to 5 volts is considered “high”

o

Interpreted as binary 1



Signals in
computers are constrained to be in one or the other



Gate

is a device that performs a basic operation on electrical signals

o

Accepts one or more input signals and produced a
single

output signal



Circuits

combine gates to perform more complicated tasks

o

In a c
ircuit, output value of one gate often serves as the input value for one or more
other gates



Three notational methods used to describe behaviour of gates and circuits:

1.

Boolean Expressions



Invented by English mathematician George Boole




Form of algebra whic
h variables and functions

outcomes

are either 0 or 1

2.

Logic Diagrams



Graphical representation of a circuit



Each gate has a specific graphical symbol

3.

Truth Tables



Defines that function of a gate by listing all possible input combinations that a
gate could en
counter, along with corresponding output

4.2 Gates



Gates are sometimes referred to as logic gates because each performs just one logical
function

o

Accepts 1 or more input value and produces a single output value


NOT Gate



Accepts one input value



Sometimes
referred to as an inverter because it inverts the input value

(0 into 1 OR 1 into 0)


AND Gate



Accepts two input signals

o

Boolean Expression: X=

(A


B) or (A*B) or (AB)



OR Gate



Accepts two input signals


XOR Gate



Referred to as e
X
clusive

OR gate

o

Differ when both signals are 1, XOR produces 0 instead



Accepts two input signals


NAND Gate



Opposite of AND gate

o

Outputs of AND are reversed

o

Like putting AND outputs into a NOT gate



Accepts two input signals

o

Boolean Expression: X=

(A


B)’ or (A*B)’ or (AB)’



NOR Gate



Opposite of OR gate

o

Outputs of OR are reversed

o

Like putting Or outputs into a NOT gate



Accepts two input signals


Review of Gates

NOT gate inverts input values

AND gate produces 1 if both inputs are 1

OR gates produces
1 if one or the other or both inputs are 1

XOR gates produces 1 if one or the other (but NOT both inputs) are 1

NAND gate produces opposite of AND gates

NOR gates produces opposite of OR gates


Gate with More Inputs



Gates can accept three or more input val
ues

o

AND gates produces an output of 1 if all values are 1

o

OR gates produces an output of 1 if any of the values are 1


4.3 Constructing Gates


Transistors



A gate uses one or more transistors to establish how the input values map to the output value



Transistor is a device that acts, depending on the voltage level of the input signal, either as a
wire that conducts electricity or as a resistor that blocks the flow of electricity

o

Had no moving parts, yet acts as a switch

o

Made of semiconductor material,
which is neither a good conductor of electricity or
good insulator



Usually silicon is used





Has three terminals

1.

A Source



Produces a high voltage value

2.

A Base



Regulates a gate that determines whether the connection between the source
and ground is made



I
f source signal is grounded, it is pulled down to 0 volts



If the base does not ground the source, it remains high (5 volts)

3.

An Emitter



Typically connected to ground wire



Output line is usually connected to source line



If source is pulled down to the ground

by the transistor



Output signal is low, binary 0



If source remains high, so does the output signal, binary 1



Transistor is either ON producing high output signal or OFF producing low output signal



Output is determined by base electrical signal



If base sig
nal is high, the source signal is grounded, which turns the transistor
off



If base signal is low, the source signal stays high, the transistor on



Easiest gates to produce with transistors are NOT, NAND and NOR



To produce a AND/OR gate



Take a NAND/OR gate a
nd pass it through a NOT gate



However, they are more complicated to produce


4.4 Circuits



Circuits can be

o

Combinational circuits



The input values
explicitly

determine the output

o

Sequential circuits



The output is a function of the input values as well as t
he existing state of the
circuit



**
READ COMBIANTION CIRCUITS on page 102
-
103

for two examples/explanation

o

Two examples demonstrate circuit equivalence

and how two gates work together




Boolean algebra properties



Adders



Addition operations are carried
out by special circuits called adders



Adding two binary digits could produce a carry value (1+1=10 in base 2, therefore carry 1)

o

Circuit that computes the sum and produced the carry bit is called
half adder



Sum output corresponds to XOR gate



Carry output c
orresponds to AND gate



Does not take into account possible carry values into calculation



Full adder

takes into consideration of carry
-
in values


Multiplexers



Often referred to as
mux

is a general circuit that produced a single output signal

o

Selects which

input signal to use as an output signal based on the value represented
by a few more input signals, called
select signals

or
select control lines

o

**READ p
age 107 for multiplexer example




A circuit called a
demultiplexer (demux)

performs the opposite
operation

o

Takes a single input and routes it to one of 2
n

outputs, depending on the values of the
n control lines


4.5 Circuits as Memory



These circuits are sequential circuit because the output of the circuit also serves as input to
the circuit

o

S
-
R latch



Stores a single binary digit of 1 or 0



**READ page 108 for
explanation
of NAND circuit used to store memory



4.6 Integrated Circuits



Integrated circuits (IC) also called a chip is a piece of silicon on which multiple gates have
been embedded

o

Silicon pie
ces are mounted on a plastic or ceramic package with pins along the edges
that can be soldered onto circuit boards or inserted into sockets

o

Each pin connects to input or output of a gate or to power or ground



IC are classified by number of gates they conta
in

Abbreviation

Name

Number of Gates

SSI

Small
-
Scale Integration

1 to 10

MSI

Medium
-
Scale Integration

10 to 100

LSI

Large
-
Scale Integration

100 to 100,000

VLSI

Very
-
Large
-
Scale Integration

More than 100,000



Larger IC chips have gates that are combine
to create complex circuits that require few input
and output values (Multiplexers)

o

Allows chip to have 100,000+ gates



4.7 CPU Chips



Most important IC is the central processing unit (CPU)

o

Each CPU chip contains large number of pins through which all
communication in a
computer system occurs