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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Chapter 1

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.

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Chapter 1

CPE/EE 422/522

1.3 More Boolean Algebra and Algebraic Simplification

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Chapter 1

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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Chapter 1

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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