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
š 1=š“ āšµ āš¶=( š“ āšµ ) āš¶=š“ ā (šµ āš¶ )=š“ āšµ āšµ āš¶=( š“ āšµ ) ā (šµ āš¶ )
Application of Sum of Products
š 1=š“ āšµ āš¶=( š“ āšµ ) āš¶=š“ ā (šµ āš¶ )=š“ āšµ āšµ āš¶=( š“ āšµ ) ā (šµ āš¶ )
Digital Logic Gates
2-Input AND GateNAND INV
NAND INV
2-Input OR Gate
NOR INV
NOR INV
Universal Gates
ā¢ NAND and NOR are easier to build than AND and OR
ā¢ 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 xā 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
Factoringāthe first & third terms above haveAC in common, which can be factored out:
Since B + B = 1, thenā¦
z = A(C + B)
Topics for Quiz 1
ā¢ Date: 3/8/2012ā In classā No Make-Up
ā¢ Number Conversionā¢ Arithmetic Operationsā¢ Complementsā¢ Signed Binary Numbersā¢ Addition/Subtractionā¢ Boolean Algebraā¢ Logic Gatesā¢ Sum of Productsā¢ Circuit Simplifications
Example 1
Example 2