# Looking for a good book on Boolean Algebra

Discussion in 'Electronic Basics' started by Newberry, Sep 28, 2006.

1. ### NewberryGuest

Hi, I am looking for a good book on Boolean Algebra and Switching
Circuits, preferably one that covers diagnostics e.g. Path
Sensitization etc. Any recommendations? Thanks in advance.

2. ### John LarkinGuest

What is path sensitization? All the google hits I get lead to
abstracts of expensive journal articles, which hints at an academic

As a working electronics designer, I don't use boolean algebra.

John

3. ### John LarkinGuest

Which is one of the things I do.

John

4. ### DanaGuest

It is used for digital logic design.

5. ### Rich GriseGuest

Boolean Algebra:

0 AND 0 = 0
0 AND 1 = 0
1 AND 0 = 0
1 AND 1 = 1

0 OR 0 = 0
1 OR 0 = 1
0 OR 1 = 1
1 OR 1 = 1

NOT 1 = 0
NOT 0 = 1

Cheers!
Rich

6. ### John LarkinGuest

Chapter 8 of AoE is about all you really need. It's rare nowadays to
design and minimize big hunks of gate-level logic, although it's handy
to generally understand the principles. What's more important is that
the logic intent be expressed (in a schematic or hdl) clearly and
correctly than that it be crushed into a minimal form. CPLDs use
sum-of-products logic, and FPGAs use lookup tables, and both use
compilers that read your intent and then do their own thing to
implement it, so classic academic boolean algebra and Karnaugh mapping
are starting to look quaint.

John

7. ### PuckdropperGuest

(View in fixed font.)

Almost:

AND *
OR +
NOT '

A*B = AB
0 0 0
0 1 0
1 0 0
1 1 1

A+B'
0 0 1
0 1 0
1 0 1
1 1 1

There you have it in a nutshell. Everything else is just a theorem or
application of mathematical laws. You can distribute, pull factors out,
etc just like regular algebra.

Puckdropper

8. ### Homer J SimpsonGuest

Or a good way to learn is to track down a copy of Rocky's Boots and play.
You can find at least the Apple version on the web to run on an Apple
emulator. Then move on to Robot Odyssey.

9. ### JamieGuest

you forgot XOR.

10. ### ClaudeGuest

Boole's work which inspired the mathematical definition concerned
algebras of sets, involving the operations of intersection, union and
complement on sets. Such algebras obey the following identities where
the operators ^, V, - and constants 1 and 0 can be thought of either as
set intersection, union, complement, universal, empty; or as two-valued
logic AND, OR, NOT, TRUE, FALSE; or any other conforming system.

a ^ b = b ^ a a V b = b V a (commutative laws)
(a ^ b) ^ c = a ^ (b ^ c)
(a V b) V c = a V (b V c) (associative laws)
a ^ (b V c) = (a ^ b) V (a ^ c)
a V (b ^ c) = (a V b) ^ (a V c) (distributive laws)
a ^ a = a a V a = a (idempotence laws)
--a = a
-(a ^ b) = (-a) V (-b)
-(a V b) = (-a) ^ (-b) (de Morgan's laws)
a ^ -a = 0 a V -a = 1
a ^ 1 = a a V 0 = a
a ^ 0 = 0 a V 1 = 1
-1 = 0 -0 = 1

Look here: http://eom.springer.de/b/b016920.htm

--

50% of all statistics are wrong. The rest don't matter.

Claude Hopper

11. ### JeffMGuest

1 AND 1 AND 1 is 3
(...or were The Beatles wrong?)

12. ### Homer J SimpsonGuest

ELECTRONICS 09 - --- "Bebop to the Boolean Boogie - Unconventional Guide
to Electronics 2nd ed. - C. Maxfield (2002) WW.pdf"

is currently posted on (along with many,
many more related books!)