Digital Logic Gates
Sum of Products (Review)
Procedure:
1. Form a minterm for each combination of the variables that produces a 1
2. 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
𝑓1 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶
Application of Sum of Products
𝑓1 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶
Digital Logic Gates
2-Input AND Gate
NAND
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 PseudoRandom Numbers
Reference: http://en.wikipedia.org/wiki/Linear_feedback_shift_register
logic.ly/demo
Circuit Simplification Example
Solution
Factoring—the first & third terms above have
AC 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
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Number Conversion
Arithmetic Operations
Complements
Signed Binary Numbers
Addition/Subtraction
Boolean Algebra
Logic Gates
Sum of Products
Circuit Simplifications
Example 1
Example 2