Transcript Boolean Functions and Gates

Department of Computer Science and Information Engineering
National Cheng Kung University
Fundamental of Digital Logic (1)
Digital Integrated Circuit Design Laboratory
Outline
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Boolean Algebra:
Boolean Functions/ Logic Functions and Gates
Theorems and Properties of Boolean Algebra
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Practices:
Introduction of Solderless Breadboard
Lab practices
Department of Computer Science and Information Engineering
National Cheng Kung University
Boolean Algebra
Digital Integrated Circuit Design Laboratory
Boolean Functions and Gates (1/6)
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Boolean Functions and Gates (2/6)
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AND
F = A‧B = AB
Boolean Functions and Gates (3/6)
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OR
F=A+B
Boolean Functions and Gates (4/6)
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Boolean Functions and Gates (5/6)
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Boolean Functions and Gates (6/6)
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Exclusive-OR (XOR)
F = AB’ + A’B = A ⊕ B
Example
The Boolean Function of F1 = x + y’z
Theorems and Properties of Boolean Algebra
Single Variable
Theorems
Two- and ThreeVariable
Properties
Examples (1/3)
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F1(x, y, z) = x’y’z + x’yz + xy’
= x’z(y’ + y) + xy’
= x’z + xy’
Examples (2/3)
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F2(x, y) = x(x’ + y)
= xx’ + xy
= 0 + xy
= xy
Examples (3/3)
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F3(x, y) = (x’ + y’) ’ = xy (DeMorgan)
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F4(x, y) = (x’y’)’ = x + y (DeMorgan)
Department of Computer Science and Information Engineering
National Cheng Kung University
Practices
Digital Integrated Circuit Design Laboratory
Introduction of Solderless Breadboard

Solderless Bredboard is a convenient kit for lay outing circuits without
any soldering work. It is very useful for circuit test and modification
during practical training.
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Components in lab can be reused with breadboard.
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Normally, component’s pins are inserted into holes on breadboard.
Every five holes are connected together by a brass strip under plastic
cover. One of holes is connected to component’s pin and the other
holes are for circuit connection with jumpers.
Top View of Solderless Breadboard
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Different types of Breadboards
Example: Connection with 74LS00 Chip
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Example
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VCC & GND must be connected!!
Lab I (1/2)
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Equipment:
Names
Amount
Solerless Breadboard
×1
74LS00
×1
74LS04
×1
74LS08
×1
74LS32
×1
Lab I (2/2)
1. Please utilize AND and OR gates to demonstrate the Boolean Function
of:
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
X=A‧B
X=A + B
2. Please finish the following circuit with Truth Table.
Lab II
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Please use Boolean Theorems and Properties to simplify the following
functions, and finish circuits with breadboard and Truth Tables.
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
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F1(A, B) = (A + B)’(A’ + B’)
F2(A, B) = A’+ AB
Equipment:
Names
Solerless Breadboard
74LS04
74LS08
74LS32
Amount
×1
×1
×1
×1
74LS00
74LS04
74LS08
74LS32