Digital Logic Help Page

The XOR and XNOR symbols (circled plus and dot, respectively) are small graphics that may not display clearly.

Digital Logic Gates

Name

Graphic Symbol

Algebraic Form

Truth Table

AND

F = xy

x	y	F
0	0	0
0	1	0
1	0	0
1	1	1

F = x + y

x	y	F
0	0	0
0	1	1
1	0	1
1	1	1

Invert (NOT)

F = x'

x	F
0	1
1	0

Buffer

F = x

x	F
0	0
1	1

NAND

F = (xy)'

x	y	F
0	0	1
0	1	1
1	0	1
1	1	0

NOR

F = (x + y)'

x	y	F
0	0	1
0	1	0
1	0	0
1	1	0

XOR

F = x

x	y	F
0	0	0
0	1	1
1	0	1
1	1	0

XNOR (EQL)

F = x

x	y	F
0	0	1
0	1	0
1	0	0
1	1	1

Postulates and Theorems of Boolean Algebra

Identity	x + 0 = x	x · 1 = x
	x + 1 = 1	x · 0 = 0
	x + x = x	x · x = x
Complement	x + x' = 1	x · x' = 0
Involution	(x')' = x
Commutative	x + y = y + x	xy = yx
Associative	x + (y + z) = (x + y) + z	x(yz) = (xy)z
Distributive	x(y + z) = xy + xz	x + yz = (x + y)(x + z)
DeMorgan	(x + y)' = x'y'	(xy)' = x' + y'
Absorption	x + xy = x	x(x + y) = x

Flip-Flop Characteristic Tables

D Flip-Flop

T Flip-Flop

D	Q(t+1)
0	0	Reset
1	1	Set

T	Q(t+1)
0	Q(t)	No change
1	Q'(t)	Toggle

SR Flip-Flop

JK Flip-Flop

S	R	Q(t+1)
0	0	Q(t)	No change
0	1	0	Reset
1	0	1	Set
1	1	?	Illegal

J	K	Q(t+1)
0	0	Q(t)	No change
0	1	0	Reset
1	0	1	Set
1	1	Q'(t)	Toggle

Flip-Flop Exciation Tables

D Flip-Flop

T Flip-Flop

Q	Q(t + 1)	D
0	0	0
0	1	1
1	0	0
1	1	1

Q	Q(t + 1)	T
0	0	0
0	1	1
1	0	1
1	1	0

SR Flip-Flop

JK Flip-Flop

Q	Q(t + 1)	S	R
0	0	0	X
0	1	1	0
1	0	0	1
1	1	X	0

Q	Q(t + 1)	J	K
0	0	0	X
0	1	1	X
1	0	X	1
1	1	X	0

Send comments and suggestions to: Dr. Charles S. Tritt
Version 1.0
This page last updated 3/8/97