Chapter 4

Gates and Circuits

Integrated Circuits aka CHIPS

• What’s in this thing????

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Chapter Goals

• How to make a gate from transistors

• How to make integrated circuits using

gates

• The basic gates and their behavior

• How gates are combined into (useful)

circuits

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Chapter Goals

• Describe gates and circuits using:

– Boolean expressions

– Truth Tables

– Logic Diagrams

• Understand half adders, full adders, and

binary addition circuits

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Computers and Electricity

• TransistorA device that can be used to

make gates

• Gate A device that performs a basic

operation on bit(s)

• Circuits Gates combined to perform more

complicated tasks

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Computers and Electricity

• 3 ways to describe the same thing

– Boolean expressions

– logic diagrams

– truth tables

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Computers and Electricity

• Boolean expressions A mathematical

notation for expressing TRUE/FALSE logic

• Example: F = AB + C

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Computers and Electricity

• Logic diagram A graphical

representation of a circuit

Each type of gate is represented by a specific

graphical symbol

• Truth table A table showing all possible

input value and the associated output

values

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Gates

• Let’s examine the processing of the following

six types of gates

– NOT

– AND

– OR

– XOR

– NAND

– NOR

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NOT Gate

• A NOT gate accepts one input value

and produces one output value

• Aka “an inverter”

Figure 4.1 Various representations of a NOT gate

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AND Gate

• 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

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OR Gate

• 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

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

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Constructing Gates

• Transistor A device that acts as a switch, either

open or closed (on or off)

– A transistor has no moving parts, yet acts like

a switch

– It is made of a semiconductor material, which is

neither a particularly good conductor of electricity,

such as copper, nor a particularly good insulator, such as rubber

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Constructing Gates

• Transistor terminals

– Source

– Base

– Emitter

• If the electrical signal is

grounded, it is allowed to

flow through an alternative

route to the ground (literally) where it can do no harm

Figure 4.8 The connections of a transistor

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Constructing Gates

• It turns out that, because the way a transistor

works, the easiest gates to create are the NOT,

NAND, and NOR gates

Figure 4.9 Constructing gates using transistors

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Combinational Circuits

• Consider the following Boolean expression A(B + C)

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Page 101

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Adders

• At the digital logic level, addition is

performed in binary

• Addition operations are carried out

by special circuits called, appropriately,

adders

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A Half Adder

• Recall that 1 PLUS 1 = 10 in base two

• In other words: 0 with a carry of 1

Inputs Outputs

A B Carry Sum

0 0 0 0

0 1 0 1

1 0 0 1

1 1 1 0

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Half Adder Circuit

• Two Boolean

expressions:

sum = A ⊕ B

carry = AB

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A Full Adder

• A circuit called a full adder takes the

carry-in value into account

Inputs Outputs

A B Carry In

Carry-

Out Sum

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Integrated Circuits

• We can combine 4 full adders to make a

Four-bit Adder Circuit (about 60

transistors)

Integrated Circuits aka CHIPS

• What’s in this thing????Chip Fabrication Technology

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Integrated Circuits

• Integrated circuit (also called a chip) A

piece of silicon on which many gates have

been embedded

“Silicon Valley”

• Sand is mostly Silicon Dioxide

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“Silicon Valley”

• Silicon Dioxide ingots and wafers

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“Silicon Valley”

• Photolithography “Printed” with lots of

copies of some circuit

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Integrated Circuits aka CHIPS

• What’s in this thing????Computer Architecture: Combining Abstractions into larger

Abstractions

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Transistors and Gates

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Integrated Circuits

An simple chip containing 4 independent

NAND gates (about 8 transistors)

Integrated Circuits

• A four-bit Full Adder Circuit

Integrated Circuits

• An Arithmetic Logic Unit (ALU) has

adders and other things in it

Integrated Circuits

• A simple Central

Processing Unit, or

CPU has an ALU

and other things

• Take Engineering

303 Digital Logic

Design!!

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CPU Chips

• A recent CPU chip (Intel Nehelem) 731

Million transistors

The Future of the IC

• Global Competition

• Further Integration (ARM)

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