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Fundamental of Digital Logic (1)
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Outline Boolean Algebra: Boolean Functions/ Logic Functions and Gates
Theorems and Properties of Boolean Algebra Practices: Introduction of Solderless Breadboard Lab practices
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Boolean Algebra
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Boolean Functions and Gates (1/6)
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Boolean Functions and Gates (2/6)
F = A‧B = AB
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Boolean Functions and Gates (3/6)
OR F = A + B
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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)
Exclusive-OR (XOR) F = AB’ + A’B = A ⊕ B
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Example The Boolean Function of F1 = x + y’z
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Theorems and Properties of Boolean Algebra
Single Variable Theorems Two- and Three- Variable Properties
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Examples (1/3) F1(x, y, z) = x’y’z + x’yz + xy’ = x’z(y’ + y) + xy’
= x’z + xy’
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Examples (2/3) F2(x, y) = x(x’ + y) = xx’ + xy = 0 + xy = xy
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Examples (3/3) F3(x, y) = (x’ + y’) ’ = xy (DeMorgan)
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Practices
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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. Components in lab can be reused with breadboard. 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.
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Top View of Solderless Breadboard
Different types of Breadboards
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Example: Connection with 74LS00 Chip
VCC & GND must be connected!!
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Lab I (1/2) Equipment: Names Amount Solerless Breadboard ×1 74LS00
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Lab I (2/2) 1. Please utilize AND and OR gates to demonstrate the Boolean Function of: X = A ‧ B X = A + B 2. Please finish the following circuit with Truth Table.
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Lab II Please use Boolean Theorems and Properties to simplify the following functions, and finish circuits with breadboard and Truth Tables. F1(A, B) = (A + B)’(A’ + B’) F2(A, B) = A’+ AB Equipment: Names Amount Solerless Breadboard ×1 74LS04 74LS08 74LS32
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74LS00
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74LS04
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74LS08
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74LS32
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