Understanding Binary Operations

From: Michael Current (aa700@cleveland.Freenet.Edu)
Date: 01/28/92-10:33:39 PM Z

From: aa700@cleveland.Freenet.Edu (Michael Current)
Subject: Understanding Binary Operations
Date: Tue Jan 28 22:33:39 1992

Reprinted from the A.C.E.C. BBS (614)-471-8559

  Understanding Binary Operations

The 6502 Processor, the CPU which
all Atari, Apple, and Commodore
8-bit computers use, supports three
bit manipulation functions.  These
functions can be very powerful in
various circumstances--in both
BASIC and especially Machine
Language.  Though Atari BASIC does
not truly support these functions,
BASIC XE and other similar
extentions of BASIC do offer them
to the BASIC user.  It is assumed
throughout this article that the
user is familiar with binary and
decimal, as well as conversions
between them.

One term must be defined before we
go further.  A "mask" is a number
that is used with any of these
operations.  You must have a mask
to use them.

First we will cover the AND
function.  This function is very
much self explanatory.  If the bit
in the original number AND in the
mask are 1, then the result will be
1.  If the bit in either of the
numbers is 0, then the resulting
bit will be 0.  To demonstrate this
(and all of these functions), we
will look at it in both binary and
decimal notation.
 Bit "Identifier":      ABCDEFGH
 Original Number:  51 = 00110011
 Mask Number:      15 = 00001111
 Resulting Value:   3 = 00000011

This says "The value 51 ANDed with
15 is 3".  As you can see, bits G
and H contain 1's in BOTH the
original number and the mask.
Because of this, bis G and H are
set in the resulting value.  Bits
E and F are not set because the
original number contains 0's in
these bits.  Bits C and D are not
set because the mask number
contains 0's in these bits.  THE
example, if you are getting input
but are not interested in whether
or not it is inverse (that is, has
an ATASCII value of 128 or more),
then you could AND the input with
127.  This will cause all input to
be normal, un-inverse characters.
In Machine Language, the format is:
AND #mask.  The Acumulator will
then be ANDed with the mask and the
result will be stored in the

Next we will deal with the OR
function.  With this function, if
a bit is set in EITHER OR BOTH the
original or the mask, then the
resulting bit will be set.  Here is
our demo of
this function:
Bit "Identifier"       ABCDEFGH
Original Value:   65 = 01000001
Mask Value:      192 = 11000000
Resulting Value: 193 = 11000001

As you can see, bit A, B, and H are
set in the resulting value.  Bit H
is set because it was set in the
original value.  Bit B is set
because it was set in BOTH the
original and the mask.  Bit A was
set because it was set in the mask.
TO FORCE SET A BIT.  If you wanted
to make all characters inverse, you
would simply OR it with the value
of 128.  In Machine Language, the
format is: ORA #mask.  The value
in the accumulator will be ORed
with the mask and the result will
be stored in the accumulator.

Finally we have the Exclusive OR
function (generally shortened to
EOR).  With the EOR function, the
bit is "flipped" if the MASK has a
1 in it.  If the mask has a 0, then
the bit is left unchanged.  Here
is the demonstration:
Bit "Identifier":      ABCDEFGH
Original Value:  193 = 11000001
Mask Value:      130 = 10000010
Resulting Value:  67 = 01000011

In the result, bit H is set because
bit H was 1 in the original.  Since
the mask contained a 0, that bit
was left unchanged.  Bit G contains
a 1.  This is because Bit G had a 0
in the original value, but since it
had a 1 in the mask, the 0 was
"flipped", thus becoming the 1.
Bits C, D, E, and F are 0 because
the 0's in the mask indicate that
the bits should be left alone, thus
the bits assume the value they had
in the original number.  Bit B is
1 since the 0 in the mask indicates
that the bit should not be changed,
and therefore remains the same as
in the original.  Bit A is 0
because the 1 in the mask says that
the original bit should be flipped:
and "flipping" a 1 will result in a
0.  This function is not used as
much as the other two functions but
can be useful in some instances.  A
very basic use of the function
would be to flip the value of a

These functions may seem a bit
complex, and they are.  However,
once mastered, these functions can
be extremely useful.  When used
properly, they can speed up
programs as well as save many many
bytes of memory.  When used in some
BASIC programs, they can condense
a multitude of IF...THENs into a
single bit manipulation.  You will
find many uses for these functions
and the time you spend learning
them will be well worth it.

                    --Craig Steiner

 Michael Current, Cleveland Free-Net 8-bit Atari SIGOp   -->>  go atari8  <<--
   The Cleveland Free-Net Atari SIG is the Central Atari Information Network
      Internet: currentm@carleton.edu / UUCP: ...!umn-cs!ccnfld!currentm
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