Bool-func

Discrete Mathematics 2 lab — a console tool for analyzing 4-variable Boolean functions. The user enters a 16-bit truth table string and can then query all standard Boolean function representations.

4 variables: x, y, z, h — 16 rows in the truth table.

Features

Option	Operation
1	Build and print the Zhegalkin polynomial (algebraic normal form)
2	Evaluate a point using the Zhegalkin polynomial
3	Build and print SDNF (perfect disjunctive normal form)
4	Build and print SKNF (perfect conjunctive normal form)
5	Evaluate a point using the BDR (binary decision diagram)
6	Print the full truth table
7	Evaluate a point using SDNF

Implementation

Input

On startup the user enters the function as a 16-character binary string (e.g. 0011010000011111), validated with std::regex.

Zhegalkin polynomial

Built using the triangle method (Pascal's triangle over GF(2)): the truth table column is XOR-reduced iteratively. Coefficients are stored in a 2D vector<vector<bool>>. The polynomial is printed in algebraic notation, e.g. F = 1 ⊕ x ⊕ xz ⊕ xyzh.

SDNF / SKNF

• SDNF: collect all minterms (rows where F = 1), write each as a conjunction of literals.
• SKNF: collect all maxterms (rows where F = 0), write each as a disjunction of literals.

Evaluation (Search_SDNF) encodes the query point as an index into the truth table.

Binary Decision Diagram (BDR)

Implemented as a binary tree of data nodes:

struct data {
    char name;      // variable: 'x', 'y', 'z', 'h', '0', '1'
    data* False;    // branch taken when variable = 0
    data* True;     // branch taken when variable = 1
};

The tree has depth 4 (one level per variable). Leaf nodes are shared BDR_F (0) and BDR_T (1) singletons. SearchBDR traverses from root to leaf by following the input bits.

Build

Visual Studio — open Dismath(2).sln

Files

File	Description
Dismath(2).cpp	main() — menu loop and input validation
BulIst.h	Class declaration + data struct
BulIst.cpp	All algorithm implementations
dismath2.pdf	Full lab report