Boolean Algebra/ Digital Logic Cheat Sheet

Digital-handel info as sets
of Is ROs Literal-single variable or its complement A, B 1) Truth Table

-better until it's not -




if working always Prod
Term-Single Literal or prod 2/move Literals A XY ,
3) Cannonical
2 Cannonical
Sum-Alg
Prod-Alp
. Sum

Prod
of Minterns
of max terms
Sum Term-Single Literal or Sum
of 2/more Literals X, X+ Y X + yz
.




same
output Analog will
degrade no
just stop 4) Minterm
,
& notation
-


List
NormalTerm
.
-
each Litera appears EXACTLY once X Y :




5) Maxterm


2)xyxz
List I notation
an 23222230 4(24(109) =

SOP-logical sum /more prodterms (+
Fut where output
Combinatorial
Logic Ent is
only
-




gate land Or output)
a
2)/more AND of an
.



OR
.




244(40)16(101) gates input
>

funt. of the
-




0 inputs
When =I no
memory only
based on current inputs

↳
,



F= GABc(2 7) + ABC + ABC + ABC + ABC + ABC
4,5 6 Local when contain variables &
diffe
DeMorgans t Adjacent
-

same
212
3
143 (24)
, , ,


16 -
40 0625 .
= =
POS-logical prod 2/move sumterms X(x + z)(y + 2)
.



form by exactly /variable X -> *
532 -50 03125 . 2)more OR gates input of an AND gate (or and cutput)
-
>
Converting
60 015625 X y + X = >. + X y :




↳70007
-
:




GABc(0 3 7) TABc 11.2 5)
when E
-



F
.

= 4 4 =



(A+ B +c) (A + B+c) (A+ B+ z) (x + y) y) (x + y) + (x + y)
.
, ,


(x
, ,

+ +
5 Bc (0 ,
1
,
3) >
- +



& 52-900019 K Map




·
S 2 8 Dexadecimal.He
Binary Decimal Octal

189 625
.




Typical Digital System
(T) blw 65-100 % Vac
missonycoveredbyitscertaina
1011110I
1 -
volt .




O(F) -

volt blw 0-35 % Va




Nu
.
189 . 625

SOP = IS
O 132
Middle 30% "invalid"
POS OS =
57 6
4
↳ Don't Care X
syste "unideal"
=

acts
·

oscillate
↓ nor

Xor odd #IS
even #15
is
- 13
I
Now Patterns ? r
Many regroup
"

does not
changefunct .
>
-


an alwaysi a

Binary 16
digit range
-




2 65 536 (A + B) # 5 AB A+




additionen
= = : =
, Decimal


Hex ↳ 240F 625
(A+ B +c) A B. A+ B +
-digit ABC =
.

- = .




- F3C7 A .




16 = 4095 Bubble Bubble-changinggate formswf DMThm
Binary pattern of XXXX XXXX .
inputo become inverted

1/11 IIII
range = .




increment = 0000 0000 .
0 0625 .




X(0) 0XX 0 = =
NAND
-Do => %
%
not X(1) X X+ X = 1 EDo G
binary
=>
0 +0 = 0 1+ 1 =
10 variables = Nor =




fundamental complete logicstate
0 +1 1 | + | + 1 = 11 (+++ 1 100
= =
X+ 1 = 1
X + (xy) xX + Yy = =
x+ y
Hex 20 = 16 + 4
I

a b & b
X(x + y) = xx(x + y) = X
19


.
a

I

I
-Logic
Gates (7 basi
00 O

"
set
of operations that
9 B
a ↳
O
G

I
i O
enable All
of boolean
evaluated
I Do
and
true when both inputs true
A B :

Nand
false if both inputs tr
A

BCD Mg to be

Binary
.




4
digit
-




o A+ B NorDo A+
when
larger
than 9 (1001)
0 -

0000 984 , 0 + 599, 0
adjust false when both inputs false true if both inputs fa
1-0001
106 when
2 -

0010
BCD - 10000100 o
carry xarE)) AGB XorE)]o A
3 -
0011 + 0101 1001 1001
⑭o true
if either but not both true
if inputs are sam


4 -

0100
I'll doi "1 false if inputs differ
5
01
adjust 910 + S10 not Do #
010 Xaraxnow can't
-




6 0110 + Ol100l10 011 0 BCD > 1001
implements negation create logic full fa
-
-




= inverter
7 -
OllI
001 old 1000 00 11 + 1000
·
4 bit
8 1000
binary
-




9 -

1001 1000 adjust ble
carry
ASCII 0 -
15 + 0000 -
1111


printing in decimal +
10(1 +d) 00010000
requires Hex
000101
-




less # 1000001
processing Ox41
-

A-o
20(2 +0) 0010 0000 -




doesn't division a 1100001 OX61 a 0
require
- -




P =
1010000 0x50 P-2

Gray Code eliminating mechanical
rotary selector in put error P-1110000 0x70p
-

.
-
z

0 -0110000 0x300-9
reorder the time B 1011
count so
onlyknowdigit
I &
changes .
: B : 110 B: 101011
E-100 010 OX 45
If more than I
changes -> missed counts mSB remains
2-110 0101 0x45

Binary Gray Code S : 0 Dil .:
6 1100 6 101 6 : /11/10
:
>
-



5 Oll -
0101 0x35