64 lines
2.2 KiB
Org Mode
64 lines
2.2 KiB
Org Mode
|
#+title: Electruth :: Truth tables
|
||
|
|
#&summary
|
||
|
|
A guide to using truth tables with electruth
|
||
|
|
#&
|
||
|
|
#+license: bysa, page
|
||
|
|
|
||
|
|
* HOWTO: Truth tables in electruth
|
||
|
|
|
||
|
|
The truth table syntax used in electruth is simple: columns are separated by
|
||
|
|
commas (but can be separated by tabs instead), and rows are separated by
|
||
|
|
newlines. The first row must contain at least one input column and at least one
|
||
|
|
output column. To specify that something is input, prefix the input variable
|
||
|
|
with a '<' character. To specify an output, use the '>' character. This is best
|
||
|
|
illustrated with an example:
|
||
|
|
#&pre
|
||
|
|
<A,<B,>out
|
||
|
|
0,0,1
|
||
|
|
0,1,0
|
||
|
|
1,0,0
|
||
|
|
1,1,1
|
||
|
|
#&
|
||
|
|
|
||
|
|
If you save this file as something.csv (.csv means it consists of
|
||
|
|
comma-separated values) and run `electruth something.csv', you should get an
|
||
|
|
output like this:
|
||
|
|
|
||
|
|
#&pre
|
||
|
|
out = or(and(not(A), not(B)), and(A, B))
|
||
|
|
#&
|
||
|
|
|
||
|
|
This makes sense, considering that the output variable `out' is only true (a
|
||
|
|
"1" in the truth table) when `out' is either not A and not B or A and B.
|
||
|
|
|
||
|
|
So, that's how you make a truth table understandable by electruth. I want to
|
||
|
|
stress that electruth's output can almost always be shortened. In the example
|
||
|
|
above, we can see that `out' is false ("0") when A or B is true -- it is false
|
||
|
|
only when A is false and B is true, and when A is true and B is false. This
|
||
|
|
construct can be shortened to fit the XOR operator, and we can say that `out'
|
||
|
|
is false when out = A XOR B. This means that `out' is true when out = NOT (A
|
||
|
|
XOR B) (in the internals of electruth, this would be written as "out =
|
||
|
|
not(xor(A, B))"). This is much shorter than "out = or(and(not(A), not(B)),
|
||
|
|
and(A, B))". To test if the two expressions really match, electruth can be used
|
||
|
|
(and this is really electruth's best part) by running this:
|
||
|
|
|
||
|
|
#&pre
|
||
|
|
electruth truthtable.csv 'out=not A xor B'
|
||
|
|
#&
|
||
|
|
|
||
|
|
which should return this:
|
||
|
|
|
||
|
|
#&pre
|
||
|
|
out_0 = or(and(not(A), not(B)), and(A, B))
|
||
|
|
out_1 = or(and(not(A), not(B)), and(A, B))
|
||
|
|
'- out_0 matches out_1? True
|
||
|
|
#&
|
||
|
|
|
||
|
|
which just confirms that it is true.
|
||
|
|
|
||
|
|
|
||
|
|
I created electruth to help me design electronic digital circuits. I don't know
|
||
|
|
what you use it for, but if you stumbled upon it because of that, I can
|
||
|
|
recommend you take a look at the programs called Ktechlab and Qucs. They can be
|
||
|
|
used for boolean logic as well.
|