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<html><head>
<title>Binary Integer Numbers</title>
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<hr>
<h1>Binary Integer Numbers</h1>
<hr>
<p>XLISP provides the <a href="../manual/xlisp.htm#binary">#b</a>
<nobr>read-macro</nobr> for binary numbers:</p>
<pre class="example">
#b0 => 0 #b1000 => 8 #b100000 => 16
#b1 => 1 #b1001 => 9 #b100001 => 17
#b10 => 2 #b1010 => 10 #b100010 => 18
#b11 => 3 #b1011 => 11 #b100011 => 19
#b100 => 4 #b1100 => 12 #b100100 => 20
#b101 => 5 #b1101 => 13 #b100101 => 21
#b110 => 6 #b1110 => 14 #b100110 => 22
#b111 => 7 #b1111 => 15 #b100111 => 23
</pre>
<p><div class="box">
<dl>
<dt>(<b>bin-string</b> <i>integer</i> [<i>all</i>])</dt>
<dd><i>integer</i> - an integer expression<br>
<i>all</i> - a boolean expression<br>
returns - the <i>integer</i> in binary form as string</dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">bin-string</font> (integer &optional all)
(if (integerp integer)
(let ((digits (or (dolist (bits '(16 32 64 128) nil)
(let ((fixnum (round (expt 2.0 (1- bits)))))
(and (plusp (1- fixnum))
(minusp fixnum)
(return bits))))
(error <font color="#880000">"integer limit not found"</font>)))
(string <font color="#880000">""</font>))
(dotimes (x digits)
(let ((digit (logand (round (expt 2.0 x)) integer)))
(setq string (strcat (if (zerop digit) <font color="#880000">"0" "1"</font>) string))))
(format nil <font color="#880000">"~a"</font> (if all string (string-left-trim <font color="#880000">"0"</font> string))))
(error <font color="#880000">"not an integer"</font> integer)))
</pre>
<p>The '<nobr>bin-string</nobr>' function converts the 'integer' argument
into binary form and returns is as a string. <nobr>If the</nobr>
optional 'all' argument is not given or
<a href="../reference/nil.htm">NIL</a>, leading zeros are not included in
the string. <nobr>If the</nobr> optional 'all' argument is
<nobr>non-<a href="../reference/nil.htm">NIL</a></nobr>, all digits of the
internal representation of the 'integer' argument, including leading zeros,
are contained in the string. This is useful for debugging integer overflow
and <nobr>bit-wise</nobr> functions.</p>
<p><div class="box">
<dl>
<dt>(<b>bin</b> <i>integer</i> [<i>all</i>])</dt>
<dd><i>integer</i> - an integer expression<br>
<i>all</i> - a boolean expression<br>
prints - the <i>integer</i> in binary form<br>
returns - the <i>integer</i> argument</dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">bin</font> (integer &optional all)
(if (integerp integer)
(format t <font color="#880000">"#b~a~%"</font> (bin-string integer all))
(format t <font color="#880000">";; not an integer~%"</font>))
integer)
</pre>
<p>The 'bin' function prints the 'integer' argument in binary form on
the screen. Together with the
<a href="../manual/xlisp.htm#binary">#b</a> <nobr>read-macro</nobr>
this can be used for interactive binary computations.</p>
<pre class="example">
> (bin 12345678)
#b101111000110000101001110
12345678
> (bin 12345678 :all)
#b00000000101111000110000101001110
12345678
> (bin 1.2345678)
;; not an integer
1.2345678
> (bin (logand #b1011 #b1101))
#b1001
9
</pre>
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