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Chapter 4
Gates and Circuits
Integrated Circuits aka CHIPS
• What’s in this thing????
4–2
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
4–3
Chapter Goals
• Describe gates and circuits using:
– Boolean expressions
– Truth Tables
– Logic Diagrams
• Understand half adders, full adders, and
binary addition circuits
4–4
Computers and Electricity
• Transistor A 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
4–5
Computers and Electricity
• 3 ways to describe the same thing
– Boolean expressions
– logic diagrams
– truth tables
4–6
Computers and Electricity
• Boolean expressions A mathematical
notation for expressing TRUE/FALSE logic
• Example:
F = AB + C
4–7
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
4–8
Gates
• Let’s examine the processing of the following
six types of gates
–
–
–
–
–
–
NOT
AND
OR
XOR
NAND
NOR
4–9
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
4–10
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
4–11
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
4–12
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
4–15
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
4–14
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
4–15
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
4–16
Combinational Circuits
• Consider the following Boolean expression A(B + C)
Page 100
Page 101
4–17
Adders
• At the digital logic level, addition is
performed in binary
• Addition operations are carried out
by special circuits called, appropriately,
adders
4–18
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
4–19
Half Adder Circuit
• Two Boolean
expressions:
sum = A  B
carry = AB
Page 103
4–20
A Full Adder
• A circuit called a full adder takes the
carry-in value into account
Inputs
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
Outputs
CarryCarry In Out
Sum
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
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
4–23
Integrated Circuits
• Integrated circuit (also called a chip) A
piece of silicon on which many gates have
been embedded
4–24
“Silicon Valley”
• Sand is mostly Silicon Dioxide
4–25
“Silicon Valley”
• Silicon Dioxide ingots and wafers
4–26
“Silicon Valley”
• Photolithography “Printed” with lots of
copies of some circuit
4–27
Integrated Circuits aka CHIPS
• What’s in this thing????
Computer Architecture: Combining Abstractions into larger
Abstractions
4–28
Transistors and Gates
4–29
Integrated Circuits
An simple chip containing 4 independent
NAND gates (about 8 transistors)
4–30
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!!
CPU Chips
• A recent CPU chip (Intel Nehelem) 731
Million transistors
4–34
The Future of the IC
• Global Competition
• Further Integration (ARM)
4–35