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

Electronics - Devices

Nov 27, 2013 (4 years and 5 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

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

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

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

Sum output corresponds to XOR gate

Carry output c
orresponds to AND gate

Does not take into account possible carry values into calculation

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

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

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