static void Main(string[] args)
{
uint[] outputIntegers = KaterynaBodnarchukTask.KateBodnarchukCase;
bool[] output = BitTools.GetOutputBool(outputIntegers);
List <Implicant> constituents = PositiveMcCluskeyMethod.GetConstituents(output);
string constituentsDisjunctionFormString =
Implicant.GetDisjunctionFormString(constituents);
Console.WriteLine("Original Function: " + constituentsDisjunctionFormString);
var minimalDisjunctionalNormalFunction =
PositiveMcCluskeyMethod.GetImplicantDisjunctionNormalForm(output);
Console.WriteLine(
"Optimized Function: "
+
Implicant.GetDisjunctionFormString(minimalDisjunctionalNormalFunction)
);
uint input = uint.Parse(Console.ReadLine());
Console.WriteLine(
"Output: "
+
ImplicantDisjunctionNormalForm.Evaluate(
minimalDisjunctionalNormalFunction,
input
)
);
Console.ReadKey();
}
public void quineTest()
{
//int[] minterms1 = new int[10] {0, 1, 2, 5, 6, 7, 8, 9, 10, 14};
int[] minterms1 = new int[] { 0, 1, 2, 5, 6, 7 };
BooleanAlgebra.Quine quine1 = new BooleanAlgebra.Quine(minterms1, 3);
List <Implicant> essential = quine1.simplify();
System.Console.WriteLine(quine1.ToString());
Console.WriteLine("The Expression is");
Console.WriteLine(Implicant.ConvertToExpression(essential));
}
internal static Implicant <T> CombineImplicants <T>(
this Implicant <T> implicantA,
Implicant <T> implicantB)
{
var variableTermMapB = implicantB
.TermSet
.ToDictionary(
keySelector: term => term.Value,
elementSelector: term => term);
var combinedMinterm = implicantA
.TermSet
.Select(termA =>
{
var variable = termA.Value;
var termB = variableTermMapB[variable];
return((termA, termB) switch
{
(PositiveTerm <T> _, NegativeTerm <T> _) => new CombinedTerm <T>(variable),
(NegativeTerm <T> _, PositiveTerm <T> _) => new CombinedTerm <T>(variable),
_ => termA
});
})
public ReducedBooleanExpression(ExpandedBooleanExpression bexpr)
{
_sortedVariables = bexpr.GetAllVariables();
ushort index = 0;
foreach (char c in _sortedVariables)
{
_alphabet[c] = index;
index++;
}
Implicant i = null;
foreach (string factor in bexpr.AsString.Split('+'))
{
i = new Implicant(this, factor);
if ((i == null) || (i.IsContradiction))
continue;
_implicants.Add(i);
}
//
CalculatePrimeImplicants();
BuildMintermToPrimeImplicantTable();
_mintermCount = _primeImplicantTable.Count();
PickFinalImplicants();
}
public static string GetSimplified(IEnumerable <LogicItem> List, int variables, bool hazardsafe = false, bool lsba = false, bool negate = false)
{
var implicants = new ImplicantCollection();
var items = (from i in List where i.Checked == true || i.Checked == null orderby i.Index ascending select i.Index).ToArray();
var careminterms = (from i in List where i.Checked == true orderby i.Index ascending select i.Index).ToArray();
foreach (var item in items)
{
var m = new Implicant();
m.Mask = LogicItem.GetBinaryValue(item, variables);
m.Minterms.Add(item);
implicants.Add(m);
}
//int count = 0;
while (Simplify(ref implicants))
{
//Populate a matrix.
bool[,] matrix = new bool[implicants.Count, items.Length]; //x, y
PopulateMatrix(ref matrix, implicants, items);
}
ImplicantCollection selected;
if (hazardsafe)
{
selected = implicants;
}
else
{
selected = SelectImplicants(implicants, careminterms);
}
return(GetFinalExpression(selected, lsba, negate));
}
public ImplicantRelationship(Implicant first, Implicant second)
{
A = first;
B = second;
}
/*
* Entry point.
*/
public static void Main(string[] args)
{
int[] input = null;
Console.WriteLine("Michael Landi\t\tComp. Architecture.");
Console.WriteLine("Boolean Simplification Program");
Console.WriteLine();
Console.Write("ENTER MINTERMS: ");
string[] minterms = Console.ReadLine().Split(' ');
Console.WriteLine();
//Parse and validate input.
try
{
input = new int[minterms.Length];
for (int i = 0; i < input.Length; i++)
{
input[i] = -1; //That way we can check for duplicate zeroes.
}
//Empty string passed.
if (minterms.Length == 0 || minterms[0].Trim() == string.Empty)
{
throw new Exception("No input.");
}
for (int i = 0; i < minterms.Length; i++)
{
int check = Int32.Parse(minterms[i]);
if (check < 0)
{
throw new Exception("Input cannot be less than zero.");
}
if (input.Contains(check))
{
throw new Exception("Input cannot contain the same minterm twice.");
}
input[i] = check;
}
Array.Sort(input);
}
catch (Exception ex)
{
Console.WriteLine("ERROR: " + ex.Message);
Environment.Exit(-1);
}
//Create initial list of minterms.
ImplicantCollection implicants = new ImplicantCollection();
foreach (int i in input)
{
Implicant m = new Implicant();
m.Mask = Convert.ToString(i, 2);
m.Minterms.Add(i);
implicants.Add(m);
}
//Simplify expressions.
int count = 0;
while (Simplify(ref implicants))
{
//Populate a matrix.
bool[,] matrix = new bool[implicants.Count, input.Length]; //x, y
PopulateMatrix(ref matrix, implicants, input);
PrintMatrix(matrix, input, ++count);
}
//Select implicants.
ImplicantCollection selected = SelectImplicants(implicants, input);
string strFinal = GetFinalExpression(selected);
Console.WriteLine();
Console.WriteLine("SIMPLIFIED EXPRESSION: ");
Console.WriteLine(strFinal);
Console.ReadKey();
}
/*
* Simplifies a givenset of implicants.
*/
private static bool Simplify(ref ImplicantCollection implicants)
{
/*
* Group by number of 1's and determine relationships by comparing.
*/
ImplicantGroup group = Group(implicants);
ImplicantRelationshipCollection relationships = new ImplicantRelationshipCollection();
for (int i = 0; i < group.Keys.Count; i++)
{
if (i == (group.Keys.Count - 1))
{
break;
}
ImplicantCollection thisGroup = group[group.Keys.ElementAt(i)];
ImplicantCollection nextGroup = group[group.Keys.ElementAt(i + 1)];
foreach (Implicant a in thisGroup)
{
foreach (Implicant b in nextGroup)
{
if (GetDifferences(a.Mask, b.Mask) == 1)
{
relationships.Add(new ImplicantRelationship(a, b));
}
}
}
}
/*
* For each relationship, find the affected minterms and remove them.
* Then add a new implicant which simplifies the affected minterms.
*/
foreach (ImplicantRelationship r in relationships)
{
ImplicantCollection rmList = new ImplicantCollection();
foreach (Implicant m in implicants)
{
if (r.a.Equals(m) || r.b.Equals(m))
{
rmList.Add(m);
}
}
foreach (Implicant m in rmList)
{
implicants.Remove(m);
}
Implicant newImplicant = new Implicant();
newImplicant.Mask = GetMask(r.a.Mask, r.b.Mask);
newImplicant.Minterms.AddRange(r.a.Minterms);
newImplicant.Minterms.AddRange(r.b.Minterms);
bool exist = false;
foreach (Implicant m in implicants)
{
if (m.Mask == newImplicant.Mask)
{
exist = true;
}
}
if (!exist) //Why am I getting dupes?
{
implicants.Add(newImplicant);
}
}
//Return true if simplification occurred, false otherwise.
return(!(relationships.Count == 0));
}
/*
* Simplifies a givenset of implicants.
*/
private static bool Simplify(ref ImplicantCollection implicants)
{
/*
* Group by number of 1's and determine relationships by comparing.
*/
var groups = (from i in Group(implicants) orderby i.Key select i).ToDictionary(i => i.Key, i => i.Value);
var relationships = new ImplicantRelationshipCollection();
for (int i = 0; i < groups.Keys.Count; i++)
{
if (i == (groups.Keys.Count - 1))
{
break;
}
var thisGroup = groups[groups.Keys.ElementAt(i)];
var nextGroup = groups[groups.Keys.ElementAt(i + 1)];
var q = from a in thisGroup from b in nextGroup where GetDifferences(a.Mask, b.Mask) == 1 select new ImplicantRelationship(a, b);
relationships.AddRange(q);
}
/*
* For each relationship, find the affected minterms and remove them.
* Then add a new implicant which simplifies the affected minterms.
*/
foreach (ImplicantRelationship r in relationships)
{
var rmList = new ImplicantCollection();
foreach (Implicant m in implicants)
{
if (r.a.Equals(m) || r.b.Equals(m))
{
rmList.Add(m);
}
}
foreach (Implicant m in rmList)
{
implicants.Remove(m);
}
var newImplicant = new Implicant();
newImplicant.Mask = GetMask(r.a.Mask, r.b.Mask);
newImplicant.Minterms.AddRange(r.a.Minterms);
newImplicant.Minterms.AddRange(r.b.Minterms);
bool exist = false;
foreach (Implicant m in implicants)
{
if (m.Mask == newImplicant.Mask)
{
exist = true;
}
}
if (!exist) //Why am I getting dupes?
{
implicants.Add(newImplicant);
}
}
//Return true if simplification occurred, false otherwise.
return(!(relationships.Count == 0));
}
public static Expr QuineMcCluskey(Expr e, IEnumerable <Expr> knownTrue)
{
HashSet <Expr> variables = new HashSet <Expr>();
Action <Expr> findVars = null;
findVars = x => {
bool isVar = true;
switch (x.ExprType)
{
case Expr.NodeType.Unary:
var eUnary = (ExprUnary)x;
if (eUnary.Op == UnaryOp.Not)
{
findVars(eUnary.Expr);
isVar = false;
}
break;
case Expr.NodeType.Binary:
var eBinary = (ExprBinary)x;
if (eBinary.Op == BinaryOp.And || eBinary.Op == BinaryOp.Or)
{
findVars(eBinary.Left);
findVars(eBinary.Right);
isVar = false;
}
break;
case Expr.NodeType.Literal:
isVar = false;
break;
}
if (isVar)
{
variables.Add(x);
}
};
findVars(e);
var useKnownTrue = knownTrue.Where(x => GetVarsVisitor.GetAll(x).All(y => variables.Contains(y))).ToArray();
var exprs = variables.ToArray();
var exprMap = exprs.Select((x, i) => new { x, i }).ToDictionary(x => x.x, x => x.i);
var truthTable = EnumBits(exprs)
.Select(bits => {
foreach (var known in useKnownTrue)
{
var knownResult = EvalVisitor.Eval(bits, exprMap, known);
if (!knownResult)
{
return(null);
}
}
return((bool?)EvalVisitor.Eval(bits, exprMap, e));
})
.ToArray();
var nextStageImplicants = new HashSet <Implicant>(truthTable
.Select((x, i) => new { bits = new Bits(i), x })
.Where(x => !x.x.HasValue || x.x.Value)
.Select(x => new Implicant(x.bits, 0, new[] { x.bits.Value })), Implicant.EqComparerInstance);
var primeImplicants = new List <Implicant>();
while (nextStageImplicants.Any())
{
var minTerms = nextStageImplicants
.GroupBy(x => x.Bits.BitCount)
.OrderBy(x => x.Key)
.ToArray();
nextStageImplicants.Clear();
Implicant[] sameBitCount1 = minTerms[0].OrderBy(x => x.DoesntMatter).ThenBy(x => x.Bits.Value).ToArray(), sameBitCount0 = null;
for (var sameBitCountIdx = 1; sameBitCountIdx < minTerms.Length; sameBitCountIdx++)
{
sameBitCount0 = sameBitCount1;
sameBitCount1 = minTerms[sameBitCountIdx].OrderBy(x => x.DoesntMatter).ThenBy(x => x.Bits.Value).ToArray();
for (int i = 0; i < sameBitCount0.Length; i++)
{
for (int j = 0; j < sameBitCount1.Length; j++)
{
var minTerm0 = sameBitCount0[i];
var minTerm1 = sameBitCount1[j];
if (minTerm0.DoesntMatter == minTerm1.DoesntMatter)
{
var diff = new Bits(minTerm0.Bits.Value ^ minTerm1.Bits.Value);
if (diff.BitCount == 1)
{
var combinedBits = minTerm0.Bits.Value & minTerm1.Bits.Value;
var combinedDoesntMatter = minTerm0.DoesntMatter | diff.Value;
var combinedCovers = minTerm0.Covers.Concat(minTerm1.Covers).OrderBy(x => x).ToArray();
var combined = new Implicant(new Bits(combinedBits), combinedDoesntMatter, combinedCovers);
nextStageImplicants.Add(combined);
sameBitCount0[i].Combined = true;
sameBitCount1[j].Combined = true;
}
}
}
}
primeImplicants.AddRange(sameBitCount0.Where(x => !x.Combined));
}
primeImplicants.AddRange(sameBitCount1.Where(x => !x.Combined));
}
primeImplicants = primeImplicants.OrderBy(x => x.Bits.Value).ThenBy(x => x.DoesntMatter).ToList();
var requiredMinTerms = truthTable
.Select((x, i) => new { x, i })
.Where(x => x.x.HasValue && x.x.Value)
.Select(x => x.i)
.ToArray();
var essentialPrimeImplicants = new HashSet <Implicant>();
for (int i = 0; i < requiredMinTerms.Length; i++)
{
var requiredMinTerm = requiredMinTerms[i];
var covers = primeImplicants.Where(x => x.Covers.Contains(requiredMinTerm)).ToArray();
if (covers.Length == 1)
{
essentialPrimeImplicants.Add(covers[0]);
}
}
var requiredPrimeImplicants = essentialPrimeImplicants.ToArray();
var nonEssentialMinTerms = requiredMinTerms.Where(x => !essentialPrimeImplicants.Any(y => y.Covers.Contains(x))).ToArray();
var nonEssentialPrimeImplicants = primeImplicants.Except(essentialPrimeImplicants).ToArray();
if (nonEssentialMinTerms.Any() && nonEssentialPrimeImplicants.Any())
{
var extraPrimeImplicants = FindOptimalImplicants(nonEssentialPrimeImplicants, nonEssentialMinTerms);
requiredPrimeImplicants = requiredPrimeImplicants.Concat(extraPrimeImplicants).ToArray();
}
var ctx = e.Ctx;
Expr eResult;
if (!requiredPrimeImplicants.Any())
{
eResult = ctx.Literal(false);
}
else
{
var requiredAndExprs = requiredPrimeImplicants
.Select(x => {
var toOr = Enumerable.Range(0, exprs.Length).Select(i => {
var mask = 1 << i;
if ((x.DoesntMatter & mask) != 0)
{
return(null);
}
var needNot = (x.Bits.Value & mask) == 0;
if (needNot)
{
return(ctx.ExprGen.Not(exprs[i]));
}
else
{
return(exprs[i]);
}
})
.Where(y => y != null)
.ToArray();
if (toOr.Any())
{
var orExpr = toOr.Aggregate((a, b) => ctx.ExprGen.And(a, b));
return(orExpr);
}
else
{
return(ctx.Literal(true));
}
})
.ToArray();
eResult = requiredAndExprs.Aggregate((a, b) => ctx.ExprGen.Or(a, b));
}
if (e.DoesEqual(eResult))
{
return(e);
}
else
{
return(eResult);
}
}
private static AndFunction ToAndFunciton(Implicant implicant)
=> new AndFunction(
implicant.Items.Select(GetInputSignFunction));