digital logic gates. sum of products (review) procedure: 1.form a minterm for each combination of...
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Digital Logic Gates
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Sum of Products (Review)
Procedure:1. Form a minterm for each combination of the variables that produces a 12. OR all the minterms.
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Three-Terminal AND Gate
F2 A B C
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
1 1 1 1
𝑓 1=𝐴 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙𝐶=𝐴 ∙ (𝐵 ∙𝐶 )=𝐴 ∙𝐵 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙ (𝐵 ∙𝐶 )
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Application of Sum of Products
𝑓 1=𝐴 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙𝐶=𝐴 ∙ (𝐵 ∙𝐶 )=𝐴 ∙𝐵 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙ (𝐵 ∙𝐶 )
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Digital Logic Gates
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2-Input AND GateNAND INV
NAND INV
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2-Input OR Gate
NOR INV
NOR INV
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Universal Gates
• NAND and NOR are easier to build than AND and OR
• NAND and NOR are used to implement AND and OR gates
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NAND/NOR
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NAND-Based OR Gate
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NOR-Based NAND Gate
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XOR/XNOR
F=1 when x≠y
F=1 when x=y
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Application of an XOR Gate
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Use a XOR to Generate Pseudo-Random Numbers
Reference: http://en.wikipedia.org/wiki/Linear_feedback_shift_register
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logic.ly/demo
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Circuit Simplification Example
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Solution
Factoring—the first & third terms above haveAC in common, which can be factored out:
Since B + B = 1, then…
z = A(C + B)
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Topics for Quiz 1
• Date: 3/8/2012– In class– No Make-Up
• Number Conversion• Arithmetic Operations• Complements• Signed Binary Numbers• Addition/Subtraction• Boolean Algebra• Logic Gates• Sum of Products• Circuit Simplifications
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Example 1
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Example 2