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# Boolean Algebra Toolbox , ver. 2.2

### Rasmus Anthin (view profile)

27 Nov 2002 (Updated )

Generate nbc and gray code, boolean evaluation and display truth-table. The "bool"-class for conveni

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Description

Boolean Algebra Toolbox is a small set of functions for easy generation of boolean nbc and gray sequences for sets of boolean variables.
[X1 X2...]=NBC(N) will generate a table of Natural Binary Code where the output is a set of bool-objects.
[X1 X2 X3]=NBC(3) yields:

» [x1 x2 x3]=nbc(3)

x1 =

0101 0101

x2 =

0011 0011

x3 =

0000 1111

and BGRAY(3) yields:

» [x1 x2 x3]=grayc(3)

x1 =

0110 0110

x2 =

0011 1100

x3 =

0000 1111

The constructor for the bool-class works as this:

» x=bool([1 inf 0 -1 0 nan])

x =

1101 01

of course, the constructor can also have a bool object as an argument.

B2H(X) is a function which converts a binary vector to hex string (length(X)=2^n is required).

The operators used are
+ : or
| : or
* : and
& : and
~ : not
' : not
/ : xor

you can use inequalities as well:
< > <= >= == ~=

some functions used by the bool class:

b2d : "bool" to decimal
b2h : "bool" to hex
display : display object
double : convert to double array
flip : flip the entire boolean object string
flip4 : flips the overall nibble position
flip4i : flips the bit positions for each nibble
flip8 : same as flip4 but for bytes
flip8i : same as flip4i but for bytes
horzcat : bit string concatenation, works with mixed objects (as [0 x1 1 nan x2])
length : length of the bit-string/bool-object
size : size of object in bits, nibbles, bytes, words, etc... depending on structure.
subsasgn : assign with indicies
subsref : pick out bits from the object string with indicies (subscripted reference).

Last but not least, the truth-table function which displays the truth-table for a boolean function with its set of variables. For instance:

» [x1 x2 x3]=nbc(3);
» func=x1'*x2+x3'/x1+x1*x2'*x3;
» btab(func,x1,x2,x3)

+-------------+----------+
| x1 x2 x3 | func(*) |
+-------------+----------+
| 0 0 0 | 1 |
| 1 0 0 | 0 |
| 0 1 0 | 1 |
| 1 1 0 | 0 |
| 0 0 1 | 0 |
| 1 0 1 | 1 |
| 0 1 1 | 1 |
| 1 1 1 | 1 |
+-------------+----------+

»

I know that there might be some strange stuff goin on with the order (little/big endian a.s.o.), which is one of the reasons I implemented the flip-functions.
Please mail me for suggestions of if you encounter any problems!

More toolboxes can be found at:

http://www.etek.chalmers.se/~e8rasmus/eng/matlab_programs.html

MATLAB release MATLAB 5.2 (R10)
11 May 2011 Pat

### Pat (view profile)

Hi - don't know what might have changed between 2007, the time of the last previous post, and R2010B that I'm using but I had add the following islogical() clause to the end of bool.m

.
.
.
elseif isbool(x)
y=x;
elseif islogical(x)
y=x;
else
error('Input must be numeric.')
end

Without this change an expression such as:

(a+b)'==a'*b'

crashes.

I could correct the code (I found that Rasmus is no longer at the email address given) but I'm new to Matlab and am now sure what the protocol is.

Comment only
02 Jan 2007 Shyang-Wen Tseng

It is very useful and saves me a few days to get the idea to program the same functions. Thank you.

21 Apr 2006 Jon Dallimore

could perhaps stand a little bit of tidying up but otherwise VERY useful. Saved me about a weeks work on my dissertation by generating grey code for me.

08 Aug 2003 Rasmus Anthin

de Morgan's theorem is easy to test:

[a b]=nbc(2);
(a+b)'==a'*b'
(a*b)'==a'+b'

In both cases matlab will respond with bool object "1".

Comment only
24 Jun 2003 deweir willie

how to work boolean algebra and demargins therem, it sames confusing.

Comment only