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<h1>Binary Operators</h1>
<p>
<img src="../../graphics/pgm_icon1.gif" border="0" alt="" />
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<p> </p>
<p class="PlainText">Binary operators require two arguments. Click on any operator in the list below for details and examples.</p>
<p class="PlainText">(See also: <a href="Ops_uni.htm" target="" title="" alt="" class="MCXref_0">Unary Operators</a> and <a href="OpsPrecedence.htm" target="" title="" alt="" class="MCXref_0">Operator Precedence</a>.)</p>
<h2>Notes about the 16-bit workspace</h2>
<p class="PlainText">Many of the operator descriptions will say something like "computes (some function) of a 16-bit number." This does not mean that the operator does not work on smaller byte or nibble values, but rather that the computation is done in a 16-bit workspace. If the value is smaller than 16 bits, the BASIC Stamp pads it with leading 0s to make a 16-bit value. If the 16-bit result of a calculation is to be packed into a smaller variable, the higher-order bits are discarded (truncated).</p>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_0" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />+   (Addition)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_0" style="display: none;">
<p> </p>
<p class="PlainText"><a name="addition"></a>The Addition operator (+) adds variables and/or constants, returning a 16-bit
result. It works exactly as you would expect with unsigned integers from 0 to 65535.
If the result of addition is larger than 65535, the carry bit will be lost. If the
values added are signed 16-bit numbers and the destination is a 16-bit variable,
the result of the addition will be correct in both sign and value.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
value1 = -99
value2 = 100
value1 = value1 + value2 ' Add the numbers
DEBUG value1 ' Show the result (1)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
value2 VAR Word
Main:
value1 = -1575
value2 = 976
value1 = value1 + value2 ' Add the numbers
DEBUG SDEC ? value1 ' Show the result (-599)
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_1" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />-   (Subtraction)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_1" style="display: none;">
<p> </p>
<p class="PlainText"><a name="subtraction"></a>The Subtraction operator (-) subtracts variables and/or constants, returning
a 16-bit result. It works exactly as you would expect with unsigned integers from 0
to 65535. If the result is negative, it will be correctly expressed as a signed
16-bit number. </p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
value1 = 199
value2 = 100
value1 = value1 - value2 ' Subtract value2 from value1
DEBUG value1 ' Show the result (99)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
value2 VAR Word
Main:
value1 = 1000
value2 = 1999
value1 = value1 - value2 ' Subtract value2 from value1
DEBUG SDEC ? value1 ' Show the result (-999)
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_2" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />*   (Multiplication)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_2" style="display: none;">
<p> </p>
<p class="PlainText"><a name="multiply"></a>The Multiply operator (*) multiplies variables and/or constants, returning
the low 16 bits of the result. It works exactly as you would expect with
unsigned integers from 0 to 65535. If the result of multiplication is larger
than 65535, the excess bits will be lost. Multiplication of signed variables
will be correct in both number and sign, provided that the result is in the
range -32767 to +32767.</p>
<p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" />
</p><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
value1 = 1000
value2 = 19
value1 = value1 * value2 ' Multiply the numbers
DEBUG value1 ' Show the result (19000)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
value2 VAR Word
Main:
value1 = 1000
value2 = 19
value1 = value1 * value2 ' Multiply the numbers
DEBUG SDEC ? value1 ' Show the result (19000)
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_3" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />**   Multiply High (Return Upper 16 Bits)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_3" style="display: none;">
<p> </p>
<p class="PlainText"><a name="multi-high"></a>The Multiply High operator (**) multiplies variables and/or constants,
returning the high 16 bits of the result. When you multiply two 16-bit
values, the result can be as large as 32 bits. Since the largest variable
supported by PBASIC is 16 bits, the highest 16 bits of a 32-bit
multiplication result are normally lost. The ** (double-star) operator gives you these upper 16 bits. For example, suppose you multiply 65000
($FDE8) by itself. The result is 4,225,000,000 or $FBD46240. The * (star, or
normal multiplication) operator would return the lower 16 bits, $6240.
The ** operator returns $FBD4.</p>
<p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" />
</p><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
value1 = $FDE8
value2 = value1 ** value1 ' Multiply value1 by itself
DEBUG $value2 ' Show upper 16 bits
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
value2 VAR Word
Main:
value1 = $FDE8
value1 = value1 ** value1 ' Multiply value1 by itself
DEBUG HEX ? value1 ' Show upper 16 bits
END
</pre>
<p class="PlainText">An interesting application of the ** operator is to multiply by a known
fractional value less than one. The fraction value is expressed in units
of 1/65536. To find the fractional ** parameter, multiply the fraction part
by 65536. Example:</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL Frac = 47554 ' = 0.72562 x 65536
SYMBOL value = W0
Test:
value = 10000
value = value ** Frac ' Multiply 10000 by 0.72562
DEBUG value ' Show result (7256)
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
Frac CON 47554 ' = 0.72562 x 65536
value VAR Word
Test:
value = 10000
value = value ** Frac ' Multiply 10000 by 0.72562
DEBUG ? value ' Show result (7256)
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_4" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />*/   Multiply Middle (Return Middle 16 Bits)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_4" style="display: none;">
<p> </p>
<p class="PlainText"><a name="multi-mid"></a>The Multiply Middle operator (*/) multiplies variables and/or constants,
returning the middle 16 bits of the 32-bit result. This has the effect of
multiplying a value by a whole number and a fraction. The whole number
is the upper byte of the multiplier (0 to 255 whole units) and the fraction is
the lower byte of the multiplier (0 to 255 units of 1/256 each). The */ (star-slash)
operator gives you an excellent workaround for the BASIC Stamp's integer-only
math. Suppose you want to multiply a value by 1.5. The whole number, and therefore
the upper byte of the multiplier, would be 1, and the lower byte (fractional part)
would be 128, since 128/256 = 0.5. It may be clearer to express the */ multiplier
in hex—as $0180—since hex keeps the contents of the upper and lower bytes separate.
</p>
<p>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" />
</p><pre class="BScode" xml:space="preserve">
value1 VAR Word
Main:
value1 = 100
value1= value1 */ $0180 ' Multiply by 1.5 [1 + (128/256)]
DEBUG ? value1 ' Show result (150)
END
</pre>
<p class="PlainText">To calculate constants for use with the */ operator, take the desired (mixed) target multiplier and multiply it by 256, then convert the result to a whole integer: INT(mixed * 256). For instance, if our target multiplier is Pi
(3.14159), the resulting constant to represent that value for the */ operator is INT(3.13159 * 256) = INT(804.25) = 804 ($0324). Notice that the upper byte is $03 (decimal 3; the whole number), and the lower
byte is $24 (decimal 36; the fractional part that means 36/256). So the constant Pi for use with */
would be $0324. This isn’t a perfect match for Pi, but the error is only
about 0.1%.</p>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_5" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />/   (Division)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_5" style="display: none;">
<p> </p>
<p class="PlainText"><a name="divide"></a>The Division operator (/) divides variables and/or constants, returning a
16-bit result. It works exactly as you would expect with unsigned integers
from 0 to 65535. Use / only with positive values; signed values do not
provide correct results. Here’s an example of unsigned division:
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /></p><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
value1 = 1000
value2 = 5
value1 = value1 / value2 ' Divide the numbers
DEBUG value1 ' Show the result (200)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
Value2 VAR Word
Main:
value1 = 1000
value2 = 5
value1 = value1 / value2 ' Divide the numbers
DEBUG DEC ? value1 ' Show the result (200)
END
</pre>
<p class="PlainText">A workaround to the inability to divide signed numbers is to have your
program divide absolute values, then negate the result if one (and only
one) of the operands was negative. All values must lie within the range of
-32767 to +32767.</p>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
sign VAR Bit ' bit to hold the sign
value1 VAR Word
Value2 VAR Word
Main:
value1 = 100
value2 = -3200
sign = value1.Bit15 ^ value2.Bit15 ' determine result sign
value2 = ABS value2 / ABS value1 ' divide absolute values
IF (sign = 1) THEN value2 = -value2 ' correct sign if negative
DEBUG SDEC ? value2 ' show the result (-32)
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_6" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />// (Modulus—Remainder of Division)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_6" style="display: none;">
<p> </p>
<p class="PlainText"><a name="modulus"></a>The Modulus operator (//) returns the remainder left after dividing one
value by another. Some division problems don’t have a whole-number
result; they return a whole number and a fraction. For example, 1000 / 6 =
166.667. Integer math doesn’t allow the fractional portion of the result, so
1000 / 6 = 166. However, 166 is an approximate answer, because 166 * 6 =
996. The division operation left a remainder of 4. The // (double-slash)
operator returns the remainder of a given division operation. Naturally, numbers
that divide evenly, such as 1000 / 5, produce a remainder of 0.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
value1 = 1000
value2 = 6
value1 = value1 // value2 ' get remainder of value1 / value2
DEBUG value1 ' show the result (4)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
value2 VAR Word
Main:
value1 = 1000
value2 = 6
value1 = value1 // value2 ' get remainder of value1 / value2
DEBUG DEC ? value1 ' show the result (4)
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_7" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />MIN   (Limit a Value to Specified Low)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_7" style="display: none;">
<p> </p>
<p class="PlainText"><a name="limit-min"></a>The Minimum operator (MIN) limits a value to a specified 16-bit positive
minimum. The syntax of MIN is:</p>
<p class="PlainText"><span class="code_in_text">Value MIN Limit
</span>
</p>
<p class="PlainText">Where <i>Value</i> is a constant or variable value to perform the MIN function
upon and <i>Limit</i> is the minimum Value that <i>value</i> is allowed to be. When used in a statement like <i>result = Value MIN Limit</i>, its
logic is, 'if <i>Value</i> is less than <i>Limit</i>, then make result =
<i>Limit</i>; if <i>Value</i> is greater than or equal to <i>Limit</i>, make
result = <i>Value</i>.' MIN works in positive math only; its comparisons are not
valid when used on two’s complement negative numbers, since the positive-integer representation of a number like -1 ($FFFF in hexadecimal or 65535 in unsigned decimal) is larger
than that of a number like 10 ($000A hexadecimal or 10 decimal). Use MIN only with unsigned
integers. Because of the way fixed-size integers work, you should be careful when
using an expression involving MIN 0. For example, result = 0 - 1 MIN 0 will result in
65535 because 0 - 1 = -1 (65535 in two's compliment math) and 65535 is greater the minimum boundary 0.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
FOR value1 = 100 TO 0 STEP -10 ' walk value1 from 100 to 0
value2 = value1 MIN 50 ' use MIN to clamp at 50
DEBUG value2 ' show "clamped" value
NEXT
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value1 VAR Word
value2 VAR Word
Main:
FOR value1 = 100 TO 0 STEP 10 ' walk value1 from 100 to 0
value2 = value1 MIN 50 ' use MIN to clamp at 50
DEBUG DEC ? value2 MIN 50 ' show "clamped" value
NEXT
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_8" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />MAX   (Limit a Value to a Specified High)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_8" style="display: none;">
<p> </p>
<p class="PlainText"><a name="limit-max"></a>The Maximum operator (MAX) limits a value to a specified 16-bit positive maximum.
The syntax of MAX is:</p>
<p class="PlainText"><span class="code_in_text">Value MAX Limit</span> <![CDATA[ ]]></p>
<p class="PlainText">...where <i>Value</i> is a constant or variable value to perform the MAX function
upon and <i>Limit</i> is the maximum value that <i>Value</i> is allowed to be. When used in a statement like <i>result = Value MAX Limit</i>, its
logic is, ‘if <i>Value</i> is greater than <i>Limit</i>, then make result =
<i>Limit</i>; if <i>Value</i> is less than or equal to <i>Limit</i>, make result =
<i>Value</i>.’ MAX works in positive math only; its comparisons are not valid when
used on two’s complement negative numbers, since the positive-integer representation
of a number like -1 ($FFFF in hexadecimal or 65535 in unsigned decimal) is larger than that of a
number like 10 ($000A hexadecimal or 10 decimal). Use MAX only with unsigned integers. Because
of the way fixed-size integers work, you should be careful when using an expression
involving MAX 65535. For example, result = 65535+1 MAX 65535 will result in 0 because 65535 + 1 = 0 (in 16-bits) and 0 is less than the maximum boundary 65535.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = W0
SYMBOL value2 = W1
Main:
FOR value1 = 0 TO 100 STEP 10 ' Walk value1 from 0 to 100
value2 = value1 MAX 50 ' Use MAX to clamp at 50
DEBUG value2 ' Show "clamped" value
NEXT
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value VAR Word
Main:
FOR value = 0 TO 100 STEP 10 ' Walk value from 0 to 100
DEBUG ? value MAX 50 ' Show "clamped" value
NEXT
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_9" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />DIG   (Returns Specified Digit of Number)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_9" style="display: none;">
<p> </p>
<p class="PlainText"><a name="digit"></a>The Digit operator (DIG) returns the specified decimal digit of a 16-bit positive
value. Digits are numbered from 0 (the right-most digit) to 4 (the left-most digit
of a 16-bit number; 0 to 65535).
</p>
<p class="PlainText">
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" />
</p><pre class="BScode" xml:space="preserve">
value VAR Word
idx VAR Nib
Main:
value = 9742
DEBUG ? value DIG 2 ' Show digit 2 (7)
FOR idx = 0 TO 4
DEBUG ? value DIG idx ' Show digits 0 - 4 of 9742
NEXT
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_10" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />REV   (Reverses specified number of bits)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_10" style="display: none;">
<p> </p>
<p class="PlainText"><a name="reverse"></a>The Reverse operator (REV) returns a reversed (mirrored) copy of a specified number
of bits of a value, starting with the rightmost bit (LSB). For instance,
%10101101 REV 4 would return %1011, a mirror image of the least significant four bits of the
value.
</p>
<p class="PlainText">
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" />
</p><pre class="BScode" xml:space="preserve">
DEBUG BIN4 ? %11001010 REV 4 ' Mirror lower 4 bits (%0101)
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_11" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" /><<   (Shifts Bits Left by Specified Amount)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_11" style="display: none;">
<p> </p>
<p class="PlainText"><a name="shfitleft"></a>The Shift Left operator (<<) shifts the bits of a value to the left a
specified number of places. Bits shifted off the left end of a number are lost;
bits shifted into the right end of the number are 0s. Shifting the bits of a
value left n number of times has the same effect as multiplying that number by 2
to the nth power. For instance 100 << 3 (shift the bits of the decimal
number 100 left three places) is equivalent to 100 * 2<sup>3</sup>.
</p>
<p>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" />
</p><pre class="BScode" xml:space="preserve">
value VAR Word
idx VAR Byte
Main:
value = %1111111111111111
FOR idx = 1 TO 16 ' loop 16 times
DEBUG BIN16 ? Value << idx ' display shifted value
NEXT
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_12" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />>>   (Shift Bits Right by Specified Amount)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_12" style="display: none;">
<p> </p>
<p class="PlainText"><a name="shiftright"></a>The Shift Right operator (>>) shifts the bits of a variable to the right a
specified number of places. Bits shifted off the right end of a number are lost;
bits shifted into the left end of the number are 0s. Shifting the bits of a value
right n number of times has the same effect as dividing that number (unsigned) by 2 to the
nth power. For instance 100 >> 3 (shift the bits of the decimal number 100 right
three places) is equivalent to 100 / 2<sup>3</sup>.</p>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
value VAR Word
idx VAR Byte
Main:
value = %1111111111111111
FOR idx = 1 TO 16 ' loop 16 times
DEBUG BIN16 ? Value >> idx ' display shifted value
NEXT
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_13" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />&   (Bitwise AND)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_13" style="display: none;">
<p> </p>
<p class="PlainText"><a name="bitwiseand"></a>The Bitwise AND (&) operator returns the bit pattern of the logical AND of each bit pair in two binary values. Each bit of these values is subject to the following logic:</p><pre xml:space="preserve"><tt>    0 & 0 = 0
    0 & 1 = 0
    1 & 0 = 0
    1 & 1 = 1</tt>
</pre>
<p class="PlainText">The result returned by & will contain 1s in only those bit positions in which
both input values contain 1s.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = B0
SYMBOL value2 = B1
SYMBOL result = B2
Main:
value1 = %00001111
value2 = %10101101
result = value1 & value2
DEBUG %result ' Show AND result (%00001101)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
DEBUG BIN8 ? %00001111 & %10101101 ' Show AND result (%00001101)
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_14" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />|   (Bitwise OR)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_14" style="display: none;">
<p> </p>
<p class="PlainText"><a name="bitwiseor"></a>The Bitwise OR (|) operator returns the bit pattern of the logical OR of each bit pair in two binary values. Each bit of the values is subject to the following logic: </p><pre xml:space="preserve"><tt>    0 | 0 = 0
    0 | 1 = 1
    1 | 0 = 1
    1 | 1 = 1</tt>
</pre>
<p class="PlainText">The result returned by | will contain 1s in any bit positions in which one or
the other (or both) input values contain 1s.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = B0
SYMBOL value2 = B1
SYMBOL result = B2
Main:
value1 = %00001111
value2 = %10101001
result = value1 | value2
DEBUG %result ' Show OR result (%10101111)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
DEBUG BIN8 ? %00001111 | %10101001 ' Show OR result (%10101111)
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_15" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />^   (Bitwise XOR)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_15" style="display: none;">
<p> </p>
<p class="PlainText"><a name="bitwisexor"></a>The Bitwise Exclusive OR operator (|) returns the bit pattern of the logical XOR of each bit pair in two binary values. Each bit of the values is subject to the following logic: </p><pre xml:space="preserve"><tt>    0 ^ 0 = 0
    0 ^ 1 = 1
    1 ^ 0 = 1
    1 ^ 1 = 0</tt>
</pre>
<p class="PlainText">The result returned by ^ will contain 1s in any bit positions in which one or
the other (but not both) input values contain 1s.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = B0
SYMBOL value2 = B1
SYMBOL result = B2
Main:
value1 = %00001111
value2 = %10101001
result = value1 ^ value2
DEBUG %result ' Show OR result (%10100110)
END
</pre>
<img src="../../graphics/bs2all_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
DEBUG BIN8 ? %00001111 ^ %10101001 ' Show OR result (%10100110)
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_16" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />&/   (Bitwise AND NOT)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_16" style="display: none;">
<p class="PlainText"> </p>
<p class="PlainText"><a name="andnot"></a>The Bitwise AND NOT operator (&/) returns the bit pattern of the logical AND NOT of each bit pair in two binary values. Each bit of the values is subject to the following logic:</p><pre xml:space="preserve"><tt>    0 &/ 0 = 0
    0 &/ 1 = 0
    1 &/ 0 = 1
    1 &/ 1 = 0</tt>
</pre>
<p class="PlainText">The result returned by &/ will contain 1s in any bit positions in which the
first value is 1 and the second value is 0.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = B0
SYMBOL value2 = B1
SYMBOL result = B2
Main:
value1 = %00001111
value2 = %10101001
result = value1 &/ value2
DEBUG %result ' Show AND NOT result (%00000110)
END
</pre>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_17" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />|/ (Bitwise OR NOT)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_17" style="display: none;">
<p class="PlainText"> </p>
<p class="PlainText"><a name="ornot"></a>The OR NOT operator (|/) returns the bitwise OR NOT of two values. Each bit of the values is subject to the following logic:</p><pre xml:space="preserve"><tt>  0 |/ 0 = 1
    0 |/ 1 = 0
    1 |/ 0 = 1
    1 |/ 1 = 1</tt>
</pre>
<p class="PlainText">The result returned by |/ will contain 1s in any bit positions in which the
first value is 1 or the second value is 0.</p>
<img src="../../graphics/bs1_inline.gif" border="0" alt="" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = B0
SYMBOL value2 = B1
SYMBOL result = B2
Main:
value1 = %00001111
value2 = %10101001
result = value1 |/ value2
DEBUG %result ' Show OR NOT result (%01011111)
END
</pre>
</div>
</div>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_18" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />^/   (Bitwise XOR NOT)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_18" style="display: none;">
<p> </p>
<p><a name="xornot"></a>The Bitwise XOR NOT operator (^/) returns the bit pattern of the logical XOR NOT of each bit pair in two binary values. Each bit of
the values is subject to the following logic:
</p><pre xml:space="preserve"><tt>    0 ^/ 0 = 1
    0 ^/ 1 = 0
    1 ^/ 0 = 0
    1 ^/ 1 = 1</tt>
</pre>
<p class="PlainText">The result returned by ^/ will contain 1s in any bit positions in which the
first value and second values are equal.</p>
<img src="../../graphics/bs1_inline.gif" border="0" /><pre class="BScode" xml:space="preserve">
SYMBOL value1 = B0
SYMBOL value2 = B1
SYMBOL result = B2
Main:
value1 = %00001111
value2 = %10101001
result = value1 ^/ value2
DEBUG %result ' Show OR NOT result (%01011001)
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_19" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />AND   (Logical AND)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_19" style="display: none;">
<p> </p>
<p class="PlainText"><a name="and"></a>The AND operator returns the logical AND of two values or expressions. Note that
in the BASIC Stamp, a non-zero value is considered True (T), zero is considered
False (F). The values/expressions are subject to the following logic:
</p><pre xml:space="preserve"><tt>    F AND F = F
    F AND T = F
    T AND F = F
    T AND T = T</tt>
</pre>
<p class="PlainText">The result returned by AND will be True or False.</p>
<img src="../../graphics/bs2all_inline.gif" border="0" /><pre class="BScode" xml:space="preserve">
score VAR Byte
avg VAR Byte
Main:
score = 93
avg = 89
IF (score > 80) AND (avg > 70) THEN
DEBUG "Promote to next grade." ' both conditions are True
ELSE
DEBUG "Consider additional tutoring." ' at least one condition is False
ENDIF
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_20" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />OR   (Logical OR)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_20" style="display: none;">
<p> </p>
<p class="PlainText"><a name="or"></a>The OR operator returns the logical OR of two values or expressions. Note that
in the BASIC Stamp, a non-zero value is considered True (T), zero is considered
False (F). The values/expressions are subject to the following logic:</p><pre xml:space="preserve"><tt>  F OR F = F
    F OR T = T
    T OR F = T
    T OR T = T</tt>
</pre>
<p class="PlainText">The result returned by OR will be True or False.</p>
<img src="../../graphics/bs2all_inline.gif" border="0" /><pre class="BScode" xml:space="preserve">
score VAR Byte
avg VAR Byte
Main:
score = 63
avg = 89
IF (score < 80) OR (avg < 70) THEN
DEBUG "Consider additional tutoring." ' at least one condition is True
ELSE
DEBUG "Promote to next grade." ' both conditions are False
ENDIF
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_21" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />XOR   (Logical XOR)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_21" style="display: none;">
<p> </p>
<p class="PlainText"><a name="xor"></a>The XOR operator returns the logical Exclusive OR of two values or expressions.
Note that in the BASIC Stamp, a non-zero value is considered True (T), zero is
considered False (F). The values/expressions are subject to the following logic:</p><pre xml:space="preserve"><tt>    F XOR F = F
    F XOR T = T
    T XOR F = T
    T XOR T = F</tt>
</pre>
<p class="PlainText">The XOR operator can be confusing at first. An easy way to remember the logic
is: <i>If one or the other is True -- but not both -- then the result is True,
otherwise the result is False.</i></p>
<p class="PlainText">The result returned by XOR will be True or False.</p>
<img src="../../graphics/bs2all_inline.gif" border="0" /><pre class="BScode" xml:space="preserve">
turnL VAR Bit
turnR VAR Bit
Main:
turnL = 0
turnR = 1
IF (turnL = 1) XOR (turnR = 1) THEN ' one or other is True
DEBUG "Turning - ", "L" + ("R" - "L" * turnR)
ELSE
DEBUG "Continue straight." ' both True or both False
ENDIF
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_22" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />ATN   (Returns Arctangent of Vector (X, Y))</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_22" style="display: none;">
<p> </p>
<p class="PlainText"><a name="arctan"></a>The Arctangent operator (ATN) returns the angle to the vector specified by X and
Y coordinate values. In the BASIC Stamp, the angle is returned in binary radians
(0 to 255) instead of degrees (0 to 359). Coordinate input values are limited from
-127 to 127 (signed bytes) as shown in the diagram below:
</p>
<p>
<center>
<img src="../../graphics/ATN_HYP.png" border="0" />
</center>
<img src="../../graphics/bs2all_inline.gif" border="0" />
</p><pre class="BScode" xml:space="preserve">
idx VAR Nib ' loop counter
xCoord VAR Byte ' x coordinate of vector
yCoord VAR Byte ' y coordinate of vector
brads VAR Word ' angle in brads
degr VAR Word ' angle in degrees
Main:
FOR idx = 0 TO 7 ' load vector data
LOOKUP idx, [ 1, 1, 0, -1, -1, -1, 0, 1], xCoord
LOOKUP idx, [ 0, 1, 1, 1, 0, -1, -1, -1], yCoord
brads = xCoord ATN yCoord ' get angle of vector
degr = brads * 180 / 128 ' convert to degrees
DEBUG DEC (idx + 1), ": ",
"ATN (", SDEC xCoord, ", ", SDEC yCoord, ")",
CRSRX, 18, "= ", DEC brads, " (", DEC degr, ")", CR
NEXT
END
</pre>
</div>
</div>
<div class="MCDropDown">
<div class="MCDropDownHead_0"><a class="MCDropDownHotSpot_0" href="javascript:void(0);" id="MCDropDownHotSpot_2082691904_23" onclick="FMCDropDown( this ); return false;"><img style="border: none;margin-right: 2px;" src="../../SkinSupport/DropDownClosed.gif" MadCap:altsrc="../../SkinSupport/DropDownOpen.gif" onload="if ( typeof( FMCPreloadImage ) == 'function' ) { FMCPreloadImage( '../../SkinSupport/DropDownOpen.gif' ); }" class="MCDropDownIcon" />HYP   (Returns Hypotenuse)</a>
</div>
<div class="MCDropDownBody" id="MCDropDownBody_2082691904_23" style="display: none;">
<p> </p>
<p><a name="hypot"></a>The Hypotenuse operator (HYP) returns the length of the hypotenuse of a right
triangle with sides of length A and B. Side length (vector) input values are
limited to -127 to 127 (signed bytes).</p>
<p> </p>
<p>
<center>
<img src="../../graphics/hyp.gif" border="0" />
</center>
</p>
<img src="../../graphics/bs2all_inline.gif" border="0" /><pre class="BScode" xml:space="preserve">
DEBUG ? 3 HYP 4 ' display hypotenuse of 5
</pre>
</div>
</div>
<p> </p>
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<p style="text-align: right;"><span class="ContactInfoProjectName">BASIC Stamp Help</span> <![CDATA[ ]]><span class="ContactInfoVersion#">Version 2.5.4</span> <![CDATA[ ]]></p>
<p style="text-align: right;">Copyright © <span class="ContactInfoCompanyName">Parallax Inc.</span></p>
<p style="text-align: right;"><span class="SystemShortDate">8/8/2012</span>
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