Lesson 2: Logic Functions and Gates

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Lesson 2 Logic Functions and Gates

• David L. Koehler

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Boolean Algebra

• Uses symbols to state a logic function.
• Symbols stand for variables and primitive (basic)
  logic operations.
• The only constants are 1 and 0.

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Boolean Algebra

• Variables have only two possible values.
• True / False
• Yes / No
• 1 / 0
• Basic operations include NOT, AND, and OR.
• Derived operations include NAND, NOR, XOR, and
  XNOR.
• Combinations are limitless.
• Variables can be called inputs
• Results can be called outputs

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NOT operation

• The output is always the opposite of the input.
• We say that the NOT operation COMPLEMENTS a
  variable.
• Write it this way
• Truth Table
• Symbol

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AND operation

• Output is HIGH only if all inputs are HIGH
• Write it this way
• Truth Table
• Symbol

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AND gate as enable/inhibit gate
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AND gate with digital waveforms
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OR operation

• Output is HIGH if any input is HIGH
• Write it this way
• Truth Table
• Symbol

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OR gate as enable / inhibit
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OR gate with digital waveforms
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NAND operation

• Output is LOW when all inputs are HIGH
• Write it like this
• Truth Table
• Symbol

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NAND gate as enable / inhibit
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NAND gate with digital waveforms
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NOR operation

• Output is LOW if any input is HIGH
• (Book is wrong in Summary on page 50)
• Write it this way
• Truth Table
• Symbol

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NOR gate as enable / inhibit
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NOR gate with digital waveforms
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XOR operation

• Output is HIGH if an ODD number of inputs are
  HIGH.
• Write it like this
• Truth Table
• Symbol

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XOR as buffer / NOT gate
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XOR with digital waveforms
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XNOR operation

• Output is LOW if an odd number of inputs is HIGH.
  (Coincidence gate)
• Write it like this
• Truth Table
• Symbol

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XNOR as buffer / NOT gate
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XNOR with digital waveforms
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Enable / Inhibit Properties
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DeMorgan

• Where you cut the complement bar, the operator
  changes.

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DeMorgan gates
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Switches as 1 and 0 Generator
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LED as a Boolean value indicator
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LED as a Boolean value indicator
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A word about LEDs

• Never directly connect an LED to an output or
  power supply because a forward biased LED is
  essentially a short circuit.
• You must limit the current to about 10 ma.
• If Vcc is 5VDC, a 470 ohm resistor works OK.
• Remember, one 470 ohm resistor in series with
  each and every LED.

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The Tristate Buffer
Also available as a NOT gate.
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LOGIC FAMILIES (74XXNN)

• LS Low-power schottky TTL
• AL Advanced Low-Power Schottky TTL
• F FAST TTL
• HC High-speed CMOS
• HCT High-speed CMOS w/TTL inputs
• LVX Low-voltage CMOS
• ABT Advanced BiCMOS (TTL/CMOS hybrid)

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IC Packages

• SOIC Small outline IC
• TSSOP Thin shrink small outline package
• PLCC Plastic leaded chip carrier
• QFP Quad flat pack
• BGA Ball grid array

All ICs must be connected to a power supply!!!!
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SOIC
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PLCC
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TSSOP
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QFP
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BGA
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Glossary

• Active High
• Active Low
• AND gate
• Ball Grid Array
• Boolean Algebra
• Boolean Variable
• Bubble
• Buffer
• Bus

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Glossary

• Chip
• Clock generator
• Coincidence gate
• Complement
• Complementary metal-oxide semiconductor (CMOS)
• DeMorgan equivalent forms
• Dual in-line package (DIP)
• Enable
• Exclusive NOR gate
• Exclusive OR gate

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Glossary

• Floating (floating node)
• High Impedance State
• Inhibit
• Integrated Circuit
• Inverter
• Large scale integrated circuit (LSI)
• Light emitting diode (LED)
• Logic function
• Logic gate

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Glossary

• Logical Product
• Logical Sum
• Medium Scale Integrated Circuit (MSI)
• NAND gate
• OR gate
• Plastic leaded chip carrier (PLCC)
• Pull-up resistor
• Quad flat pack (QFP)
• Small Outline IC (SOIC)
• Small Scale Integrated circuit (SSI)

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Glossary

• Surface-mounted technology (SMT)
• Thin Shrink small outline package (TSSOP)
• Through hole
• Transistor-transistor logic (TTL)
• Tristate Buffer
• True form
• Vcc
• Very Large Scale Integrated circuit (VLSI)