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Digital logic design cheat sheet, Assignments of Digital Electronics

University of Engineering and Technology Lahore (UETL)Digital Electronics

Ggg inbr grssb gyrf. Ttybvxd gfdxb

Typology: Assignments

2020/2021

Uploaded on 10/27/2024

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abdul-mannan-17 🇵🇰

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bg1
Logic Functions & Gates + Boolean Theorems + Karnaugh Map 5/18/2004
v1.00
©2004 Brian Mosley
E-Mail: evil_techni[email protected]
Logic Functions & Gates
Logic Gate NOT AND OR NAND NOR XOR XNOR
Symbol
Description Y is invert
of A Y = 1 if A AND B = 1 Y = 1 if A OR B = 1 Y = 0 if A AND B = 1 Y = 0 if A OR B = 1 Y = 1 if A OR B = 1, not if both = 1 Y = 0 if A OR B = 1, not if both = 1
Function
YA=
YAB=×
YAB
=
+
YAB
=
×
YAB
YAB
=
⊕
=
+
YABAB
=+
YAB
=
⊕
YABAB=+
2-Input
Truth
Table
Showing
Enable &
Inhibit
A Y
0 1
1 0
A B Y E/I
0 1 0
0 0 0 (Y=0)
Inhibit
1 1 0
1 0 1 (Y=B)
Enable
A B Y E/I
0 1 0
0 0 1 (Y=B)
Enable
1 1 1
1 0 1 (Y=1)
Inhibit
A B Y E/I
0 1 1
0 0 1 (Y=1)
Inhibit
1 1 1
1 0 0 (Y=
B
)
Enable
A B Y E/I
0 1 1
0 0 0 (Y=
B
)
Enable
1 1 0
1 0 0 (Y=0)
Inhibit
A B Y E/I
0 1 0
0 0 1 (Y=B)
Enable
1 1 1
1 0 0 (Y=
B
)
Enable
A B Y E/I
0 1 1
0 0 0 (Y=
B
)
Enable
1 1 0
1 0 1 (Y=B)
Enable
Function YABC =×× YABC
=
++ YABC
=
×× YABC YABC
=
⊕⊕
YABCABCABCABC =+++
YABC
=
⊕⊕
=
++
Y ABC ABC ABC ABC=+++
3-Input
Truth
Table
Note: A
on the
inputs or
outputs
represents
active LOW
D
A B C Y
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 0
1 1 1 1
A B C Y
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
A B C Y
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
A B C Y
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
A B C Y
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1
A B C Y
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 0
Theorems of Boolean Algebra
Commutative Double Inversion AND OR XOR
x
yyx+=+
x
x=
00x
×
= 0
x
+
= 0
x
x
⊕
=
Karnaugh Map
(K-Map)
x
yyx
×=×
DeMorgan 1
x
x
×
= 11x
+
= 1
x
x
⊕
= Two Variable Three Variable Four Variable
Associative
x
yxy
=+
xx
×
=
x
xx
+
=
0xx
⊕
=
B
B
C CCD CD CD CD
()()
x
yz xy z
++=++
x
yxy
+=
0xx
×
= 1xx
+
= 1
x
x
⊕
=
B
A 0
1
/
AB
CCD
0
1
00 01
11
10
()()
x
yz xy z=
Other Multivariable
A
0
A
B
00
Distributive
x
xy x+=
A
1
A
B
01
()
x
y z xy xz+= +
()()
x
yx z x yz++=+
A
B
11
()()
x
yw z xw xz yw yz++=+++
x
xy x y+=+
A
B
10

Partial preview of the text

Download Digital logic design cheat sheet and more Assignments Digital Electronics in PDF only on Docsity!

Logic Functions & Gates + Boolean Theorems + Karnaugh Map

v

©2004 Brian Mosley

E-Mail: [email protected]

Logic Functions & Gates

Logic Gate

NOT

AND

OR

NAND

NOR

XOR

XNOR

Symbol Description

Y is invert

of A

Y = 1 if A AND B = 1

Y = 1 if A OR B = 1

Y = 0 if A AND B = 1

Y = 0 if A OR B = 1

Y = 1 if A OR B = 1, not if both = 1

Y = 0 if A OR B = 1, not if both = 1

Function

Y

A

Y

A

B

×

Y

A

B

Y

A

B

×

Y

A

B

Y

A

B

Y

AB

A

B

Y

A

B

Y

AB

AB

2-Input

TruthTable Showing Enable &

Inhibit

A

Y

A

B

Y

E/I

(Y=0) Inhibit

(Y=B) Enable

A

B

Y

E/I

(Y=B) Enable

(Y=1) Inhibit

A

B

Y

E/I

(Y=1) Inhibit

(Y=

B

Enable

A

B

Y

E/I

(Y=

B

Enable

(Y=0) Inhibit

A

B

Y

E/I

(Y=B) Enable

(Y=

B

Enable

A

B

Y

E/I

(Y=

B

Enable

(Y=B) Enable

Function

Y

A

B

C

×

×

Y

A

B

C

Y

A

B

C

×

×

Y

A

B

C

Y

A

B

C

Y

ABC

ABC

ABC

AB

C

Y

A

B

C

Y

ABC

ABC

ABC

ABC

3-Input

TruthTable

Note: A

on the inputs or

outputs represents active LOW

D

A

B

C

Y

A

B

C

Y

A

B

C

Y

A

B

C

Y

A

B

C

Y

A

B

C

Y

Theorems of Boolean Algebra

Commutative

Double Inversion

AND

OR

XOR

x

y

y

x

x

x

x

×

x

x

x

x

Karnaugh Map

(K-Map)

x

y

y

x

×

×

DeMorgan

x

x

×

x

x

x

Two Variable

Three Variable

Four Variable

Associative

x

y

x

y

x

x

x

×

x

x

x

x

x

B

B

C

C

C D

CD

CD

C D

x

y

z

x

y

z

x

y

x

y

x

x

×

x

x

x

x

B A

/

AB

C

CD

x

yz

xy z

Other Multivariable

A

A

B

Distributive

x

xy

x

A

A

B

x

y

z

xy

xz

x

y

x

z

x

yz

A

B

x

y

w

z

xw

xz

yw

yz

x

xy

x

y

A

B