{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 15: Boolean Algebra"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 15.1: Basic_definitions_in_boolean_algebra.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//0 denotes False and 1 denotes true\n",
"b=[0,1];\n",
"//binary operation  + on the set of bits\n",
"for i=1:2\n",
"for j=1:2\n",
"k = b(i)& b(j);\n",
"disp(k)\n",
"end\n",
"end\n",
"//binary operation  * on the set of bits\n",
"for i=1:2\n",
"for j=1:2\n",
"k = b(i)| b(j);\n",
"disp(k)\n",
"end\n",
"end\n",
"//unary operation ' on the set of bits\n",
"k=~b\n",
"clear;\n",
"D=[1,2,5,7,10,14,35,70];\n",
"a=35;\n",
"b=70;\n",
"V=int32([a,b]);\n",
"thelcm=lcm(V)  //a+b=lcm(a,b)\n",
"V=int32([a,b])  \n",
"thegcd=gcd(V)  //a*b=gcd(a,b)\n",
"abar=70/a      //a'=70/a"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 15.2: Boolean_algebra_as_lattices.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"D=[1,2,5,7,10,14,35,70];\n",
"a = 2;  //a and b belong to D\n",
"b = 14;\n",
"V=int32([a,b]);\n",
"thelcm=lcm(V)\n",
"V=int32([a,b]);\n",
"thegcd=gcd(V)\n",
"abar=70/a\n",
"bbar=70/b\n",
"j=[abar,b];\n",
"h=[a,bbar];\n",
"V=int32([j])\n",
"lcm1=lcm(V)\n",
"K=int32([h])\n",
"lcm2=lcm(K)"
   ]
   }
],
"metadata": {
		  "kernelspec": {
		   "display_name": "Scilab",
		   "language": "scilab",
		   "name": "scilab"
		  },
		  "language_info": {
		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
			}
		   ],
		   "mimetype": "text/x-octave",
		   "name": "scilab",
		   "version": "0.7.1"
		  }
		 },
		 "nbformat": 4,
		 "nbformat_minor": 0
}