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Digital logic: Gates, Truth tables, logic equations
Yipeng Huang
Rutgers University
April 20, 2021
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Table of contents
Announcements
Transistors: The building block of computers
Combinational logicBasic gatesMore-than-2-input gates
3/17
Looking ahead
Class plan
1. PA5 due Monday, 4/26.2. Digital logic. Reading assignment: CS:APP Chapter 4.2. Recommended
reading: Patterson & Hennessy, Computer organization and design, appendixon "The Basics of Logic Design." Available online via Rutgers Libraries.
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Table of contents
Announcements
Transistors: The building block of computers
Combinational logicBasic gatesMore-than-2-input gates
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Computer organizationLayer cake
I SocietyI Human beingsI ApplicationsI AlgorithmsI High-level programming languagesI InterpretersI Low-level programming languagesI CompilersI ArchitecturesI MicroarchitecturesI Sequential/combinational logicI TransistorsI SemiconductorsI Materials scienceI PhysicsI Mathematics
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Why binary
Figure: Source: CS:APP
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To build logic, we need switches
Vacuum tubes a.k.a. valves
Figure: Source: By Stefan Riepl (Quark48) -Self-photographed, CC BY-SA 2.0https://commons.wikimedia.org/w/index.php?curid=14682022
Transistors
Figure: Source: Wikimedia
I The first transistor developed at BellLabs, Murray Hill, New Jeresy
I https://www.bell-labs.com/about/locations/murray-hill-new-jersey-usa/
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MOSFETs
MOS: Metal-oxide-semiconductorI A sandwich of conductor-insulator-semiconductor.
FET: Field-effect transistorI Gate exerts electric field that changes conductivity of semiconductor.
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NMOS, PMOS, CMOS
PMOS: P-type MOS
I positive gate voltage, acts as opencircuit (insulator)
I negative gate voltage, acts as shortcircuit (conductor)
NMOS: N-type MOS
I positive gate voltage, acts as shortcircuit (conductor)
I negative gate voltage, acts as opencircuit (insulator)
CMOS: Complementary MOS
I A combination of NMOS and PMOS to build logical gates such as NOT,AND, OR.
I We’ll go to slides posted in supplementary material to see how they work.
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Combinational vs. sequential logic
Combinational logic
I No internal state nor memoryI Output depends entirely on inputI Examples: NOT, AND, NAND, OR,
NOR, XOR, XNOR gates, decoders,multiplexers.
Sequential logic
I Has internal state (memory)I Output depends on the inputs and
also internal stateI Examples: latches, flip-flops, Mealy
and Moore machines, registers,pipelines, SRAMs.
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Table of contents
Announcements
Transistors: The building block of computers
Combinational logicBasic gatesMore-than-2-input gates
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NOT gate
A A
A A0 11 0
Table: Truth table for NOT gate
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AND gate, NAND gate
AB
AB
A B AB0 0 00 1 01 0 01 1 1
Table: Truth table for AND gate
AB
AB
A B AB0 0 10 1 11 0 11 1 0
Table: Truth table for NAND gate
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OR gate, NOR gate
AB
A + B
A B A + B0 0 00 1 11 0 11 1 1
Table: Truth table for OR gate
AB
A + B
A B A + B0 0 10 1 01 0 01 1 0
Table: Truth table for NOR gate
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XOR gate, XNOR gate
AB
A ⊕ B
A B A ⊕ B0 0 00 1 11 0 11 1 0
Table: Truth table for XOR gate
AB
A ⊕ B
A B A ⊕ B0 0 10 1 01 0 01 1 1
Table: Truth table for XNOR gate
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More-than-2-input AND gate
AB
AB
CABC
A B C ABC0 0 0 00 0 1 00 1 0 00 1 1 01 0 0 01 0 1 01 1 0 01 1 1 1
Table: Truth table for three-input AND gate
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More-than-2-input OR gate
AB
A + B
CA + B + C
A B C A + B + C0 0 0 00 0 1 10 1 0 10 1 1 11 0 0 11 0 1 11 1 0 11 1 1 1
Table: Truth table for three-input AND gate
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