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Chapter 4
Gates and Circuits
Integrated Circuits aka CHIPS
• What’s in this thing????
4–2
4–3
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
4–4
Chapter Goals
• Describe gates and circuits using:– Boolean expressions– Truth Tables– Logic Diagrams
• Understand half adders, full adders, and binary addition circuits
4–5
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
4–6
Computers and Electricity
• 3 ways to describe the same thing– Boolean expressions– logic diagrams– truth tables
4–7
Computers and Electricity
• Boolean expressions A mathematical notation for expressing TRUE/FALSE logic
• Example: F = AB + C
4–8
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
4–9
Gates
• Let’s examine the processing of the following six types of gates– NOT– AND– OR– XOR– NAND– NOR
4–10
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
4–11
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
4–12
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
4–15
4–14
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
4–15
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
4–16
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
4–17
Combinational Circuits
• Consider the following Boolean expression A(B + C)
Page 100
Page 101
4–18
Adders
• At the digital logic level, addition is performed in binary
• Addition operations are carried out by special circuits called, appropriately, adders
4–19
A Half Adder
• Recall that 1 PLUS 1 = 10 in base two
• In other words: 0 with a carry of 1
Inputs OutputsA B Carry Sum
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0
4–20
Half Adder Circuit
• Two Boolean expressions:
sum = A Bcarry = AB
Page 103
A Full Adder
• A circuit called a full adder takes the carry-in value into account
Inputs Outputs
A B Carry InCarry-
Out Sum0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 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
4–23
4–24
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
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
4–30
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!!
4–34
CPU Chips
• A recent CPU chip (Intel Nehelem) 731 Million transistors
The Future of the IC
• Global Competition
• Further Integration (ARM)
4–35