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 InputsOutputs ABCarrySum

4–20 Half Adder Circuit Two Boolean expressions: sum = A  B carry = AB Page 103

A Full Adder A circuit called a full adder takes the carry-in value into account InputsOutputs ABCarry In Carry- OutSum

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