Class notes EE271 (EE271) Introduction to Digital Circuits and Systems

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LECTUREI LECTURE 2



1
Basic
Logic Gates ANB D管 Out Boolean Equations
OR 秀 _
out


Algabra vares



[
NOT LInverter) : 0 1
AE - Out
,




odd parity : odd # of input → output 5
i TRUE Variables :A , ,
B
C …
, XiY ,
2




}
NOT *
Operatious : NOT , ANB , OR :



AND : X *
Y ,
X &Y
OR :
XtY

ABC TABCT ABE + ABC




Advanced Laws : ABCTABET ABETABE


X + XY = X x X
Comunutative :
xtY =
Y+ x XY =
Tx
XY + XY =
X
| 0
Associaive : x+ ( +τ) (X + Y } tE
=




x + XY =
xtY ×道 E 了 边 Y3 Z
X X

x ( x + Y) = X Distziburtive: x ( Y+ t ) = XY + XZ
| 0 xtYZ =
X Y ] Lx + Z ]
☆
( x+Y ) (x+ Y) =
x

X
x (x + Y ) =
XY

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LECTURE 4
E g
.

.
F =
XYZ + XY + XYZ
FPGA : Field prsgraumable Gate
Array
1 NAND Gate NOT ( ANDLA B ]
: ,


)+ *Y
GXY ( ztE
≥ □ O 0
-



=
-
0 -




XYtXY

→ Y( x + NOR Gate : NOT ( OR ( A B ) )
,




G F :
丫
⑦ -
□

0- -




LECTURE 3
XOR Gate : output true if odd # of iuput is true

DeMorgan ' sLaw


B (I
Y >=D -
z X t 丫
X+ Y =
xy OR AND
_




2 ) XY = * t AND E OR XNORGate: Even #
is tue
ofinput




YD
≥~ z x +
Y ,
XtY

—
” 0
|
在} 到

A ⑦ BDC
c
|
“ 0 Sum Of Proabuats LSOP ) : proaluct of SUm ( POs )


L B

F = *TYZ + XYE F = [A+B) [A + B) (A+B )

last gate 5
i OR Gate last gate is AND
gate