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Digital Logic Gates
Sum of Products (Review)
Procedure:1. Form a minterm for each combination of the variables that produces a 12. OR all the minterms.
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 )
Application of Sum of Products
𝑓 1=𝐴 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙𝐶=𝐴 ∙ (𝐵 ∙𝐶 )=𝐴 ∙𝐵 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙ (𝐵 ∙𝐶 )
Digital Logic Gates
2-Input AND GateNAND INV
NAND INV
2-Input OR Gate
NOR INV
NOR INV
Universal Gates
• NAND and NOR are easier to build than AND and OR
• NAND and NOR are used to implement AND and OR gates
NAND/NOR
NAND-Based OR Gate
NOR-Based NAND Gate
XOR/XNOR
F=1 when x≠y
F=1 when x=y
Application of an XOR Gate
Use a XOR to Generate Pseudo-Random Numbers
Reference: http://en.wikipedia.org/wiki/Linear_feedback_shift_register
logic.ly/demo
Circuit Simplification Example
Solution
Factoring—the first & third terms above haveAC in common, which can be factored out:
Since B + B = 1, then…
z = A(C + B)
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
Example 1
Example 2