CPE/EE 422/522 Chapter 1 - Review of Logic Design Fundamentals
CPE/EE 422/522
Chapter 1 - Review of Logic Design Fundamentals
Dr. Rhonda Kay Gaede
UAH
1 Electrical and Computer Engineering
UAH
Chapter 1
CPE/EE 422/522
1.1 Combinational Logic
? Combinational Logic has no control inputs. When the inputs to a combinational network change, the output changes ____________________________.
X = x1 x2... xn
Z = z1 z2... zm
x1
z1
x2
z2
xn
zm
Electrical and Computer Engineering
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Chapter 1
CPE/EE 422/522
1.1 Combinational Logic Basic Logic Gates
Electrical and Computer Engineering
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Chapter 1
CPE/EE 422/522
1.1 Combinational Logic Full Adder (Minterm Form)
Module
m-form Sum = Cout = Sum = Cout =
Electrical and Computer Engineering
Truth table
X Y Cin Cout Sum
00 0
0 0
00 1
0 1
01 0
0 1
01 1
1 0
10 0
0 1
10 1
1 0
11 0
1 0
11 1
1 1
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UAH
Chapter 1
CPE/EE 422/522
1.1 Combinational Logic Full Adder (Maxterm Form)
Module
Sum = Sum = Cout = Cout =
Electrical and Computer Engineering
Truth table
X Y Cin Cout Sum
00 0
0 0
00 1
0 1
01 0
0 1
01 1
1 0
10 0
0 1
10 1
1 0
11 0
1 0
11 1
1 1
m-form Sum = Cout =
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CPE/EE 422/522
1.2 Boolean Algebra and Algebraic Simplification
? Some routines are widely used and been pooled into subroutine libraries.
? Operating systems are programs that manage the resources of a computer for the benefit of the programs that run on that machine
? Software Categories
? Systems - OS, compilers, assemblers, etc. ? Applications - spreadsheets, text editors, etc.
Electrical and Computer Engineering
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Chapter 1
CPE/EE 422/522
1.3 More Boolean Algebra and Algebraic Simplification
Electrical and Computer Engineering
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CPE/EE 422/522
1.2 Boolean Algebra with Exclusive OR
X 1= X' X0= X XX =0
X X'= 1
X Y = Y X (Commutative law) (X Y) Z = X (Y Z) X(Y Z) = XY XZ (Distributive law) (X Y)' = X Y' = X'Y = XY + X' Y'
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CPE/EE 422/522
1.3 Karnaugh Maps
? Convenient way to simplify logic functions of 3, 4, 5, (6) variables
? Four-variable K-map
? Each square ____________________________ ? 1 ________________________________ ? 0______________________________ ? d ____________________________ ? -----------------------------------------? --------------------------------------
? adjacent cells ____________________________
Electrical and Computer Engineering
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Chapter 1
CPE/EE 422/522
1.3 Karnaugh Maps - Examples
C
B A
D
Electrical and Computer Engineering
C
B A
D
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