LOGAND?

Can someone offer some kind of explanation of what the "Log" functions do
and how to use them?

I've always wondered what LOGAND and his friends did and the "description"
of "Performs a 'logical and'" provided by the help and manuals does not
help.

TIA

 

Search the term "Boolean" or the phrase "Boolean algebra" on the web and
you'll find abundant resources. If you don't understand the definition in
Help, you probably need some more background knowledge before it can be
explained to you. This is a little like asking "how do computers work?"

 

AutoCAD and Binaries :
http://www.afralisp.com/lisp/binary_I.htm

 

You've probably noticed certain values in autocad system variables, like the
running osnap "osmode". They actually use bits to describe conditions that
occure. They don't look like bits, for they're actually converted to
integers, but they represent binary values. You may have noticed that the
values for osmode are...

0 = none
1 = endpoint
2 = midpoint
4 = center
8 = node
16 = quadrant
32 = intersection
64 = insertion
128 = perpendicular
256 = tangent
and so on...

The thing to notice is that the value none is 0 then the next value is 1 and
then the next value is double of that then double of that then double of
that and so on.

First let's examine the binary number system, since that's what log
functions work with (note that even though you supply integers, the
functions actually convert the values to binary to perform their
operations):

binary value || decimal value
=======================
0000 || 0
0001 || 1
0010 || 2
0011 || 3
0100 || 4
0101 || 5
0110 || 6
0111 || 7
1000 || 8

Now you can see what binary looks like from 0 - 8 in decimal. Of course
binary is a base 2 number system (either 1's or 0's). Notice what happens
when you shift the bit from beginning to the end of the binary number...

binary value || decimal value
=======================
0001 || 1
0010 || 2
0100 || 4
1000 || 8

With each succession in the binary place the decimal value doubles. The
interesting thing is that if you combine any of these decimal numbers you
will always create a unique binary value since the bits that are 1 appear at
different places in the binary number.

Notice:
decimal action total binary
===========================
0 + 0 + 0 + 1 = 1 = 0001
0 + 0 + 2 + 1 = 3 = 0011
0 + 4 + 2 + 1 = 7 = 0111
8 + 4 + 2 + 1 = 15 = 1111

When I add 1 the first binary bit is set to 1, now if I add 2 to that binary
number the second bit is set. And so on, as I add four to the value the 3rd
bit is set and lastly, when I add 8 then fourth bit is set.

Conversley, I can subtract bits from the binary value and unset bit
positions:

Notice:

decimal action total binary
============================
(8 + 4 + 2 + 1) - 0 = 15 = 1111
(8 + 4 + 2 + 1) - 1 = 14 = 1110
(8 + 4 + 2 + 1) - 2 = 13 = 1101
(8 + 4 + 2 + 1) - 4 = 11 = 1011
(8 + 4 + 2 + 1) - 8 = 7 = 0111

So this is how you set bits. The next bit is always double of the previous
bit, likewise the previous bit is always half of the next bit.

So how is this usefull in programming? Well, as you can see you can set a
series of bits within a binary number. Then later you can check to see
which bits are set and which bits are not set. These act like switches in
your program. 1 = switch on, 0 = switch off:

Imagine the following as a switch where 1 is on and 0 is off:

The Switch:
-------------------------------
| 0 | 0 | 0 | 0 | All switch buttons are off so
the value is 0
-------------------------------

-------------------------------
| 0 | 0 | 0 | 1 | The first button is set so the
value is 1
-------------------------------

-------------------------------
| 0 | 0 | 1 | 1 | The first and second buttons
are set so the value is 1 + 2 = 3
-------------------------------

-------------------------------
| 0 | 1 | 1 | 1 | The first, second and third
buttons are set so the value is 1 + 2 + 4 = 7
-------------------------------

O.K. so back to your question, what are the log functions for? They perform
two vary critical functions for working with binary bit sets. The two
functions are AND and OR. Since we first worked with adding bits together,
lets look at the OR function, LOGIOR which stands for logical OR. If I have
two switches, each with 4 buttons and I want to check to see which buttons
are on for both switches then I use the logior function:

The logical OR performs an OR where 1 is True and 0 is False. Let's keep it
simple and use two bits only to compare. The OR function evaluates the OR
for the first bit of the first value against the first bit of the second
value. Then the second bit of the first value against the second bit of the
second value and so on.

Examine the following:

binary decimal
------------------------------------------
value1 0000 = 0
value2 0001 = 1
------------------------------------------
OR result 0001 = 1


binary decimal
------------------------------------------
value1 0001 = 1
value2 0001 = 1
------------------------------------------
OR result 0001 = 1


binary decimal
------------------------------------------
value1 0010 = 2
value2 0001 = 1
------------------------------------------
OR result 0011 = 3


binary decimal
------------------------------------------
value1 0011 = 3
value2 0001 = 1
------------------------------------------
OR result 0011 = 3

The OR is useful for adding a bit to an already created bit set. It will
just simply, given two switches (bit sets), determine which buttons are on
for both switches and return a value of all the buttons that were on for
both.

Now for the final part, the LOGAND function. It is useful for checking
wether a button is on in a switch (bit set). It campares a bit you supply
(or set of bits) against a bit set to see wether the bit is in the bit set.
Notice, if it doesn't find the bit in the bit set it returns zero. You can
then check the result of the logand using the (not (zerop (logand <bit>
<bitset>))) function to see wether the bit is set.

Examine the following:

binary decimal
------------------------------------------
value1 0000 = 0
value2 0001 = 1
------------------------------------------
AND result 0000 = 0


binary decimal
------------------------------------------
value1 0001 = 1
value2 0001 = 1
------------------------------------------
AND result 0001 = 1


binary decimal
------------------------------------------
value1 0010 = 2
value2 0001 = 1
------------------------------------------
AND result 0000 = 0


binary decimal
------------------------------------------
value1 0011 = 3
value2 0001 = 1
------------------------------------------
AND result 0001 = 1


binary decimal
------------------------------------------
value1 0111 = 7
value2 0011 = 3
------------------------------------------
AND result 0011 = 3


binary decimal
------------------------------------------
value1 1111 = 15
value2 0010 = 2
------------------------------------------
AND result 0010 = 2

And that's it. I hope this helps!

Devin

 

Check out Frank Oquendo's excellent article "Working with Bits" at
AcadX.com.
http://code.acadx.com/articles/001.htm , it really explains this well.

HTH,
Jeff

 

Pretty good explanation! I already understood it but I just wanted to say
"Hats off to you!" for taking the time to be that thorough.

 

Thanks Eric.

 

Thanks Devin.

That was very thorough and very well written. I already understood the
concept of how bits work---but I never learned how to use the log function
(or what they were for).

When I posted my question, I was figuring that someone would point me to a
tutorial somewhere. But instead, you wrote one for me. I appreciate your
taking the time to do so!

 

Your welcome.