# Examples of Boolean minimization

#### cahlucas

Joined Dec 16, 2019
5
Hello everyone,
In connection with the development of a program for Boolean minimization, think e.g. to Quine-McCluskey, I need examples and their correct solution so that I can check my program for correct operation. The number of variables may not exceed 20, and preferably between 4 and 10. The examples may be presented in this form (see the truth table below) : CD'+A'BC'+AC'D (C AND (NOT D) OR (NOT A) AND B AND (NOT C) OR A AND (NOT C) AND D). I would like to receive a response from you. Kind regards, Karel.
Code:
 i  A B C D  X
0  0 0 0 0  0
1  0 0 0 1  0
2  0 0 1 0  1
3  0 0 1 1  0
4  0 1 0 0  1
5  0 1 0 1  1
6  0 1 1 0  1
7  0 1 1 1  0
8  1 0 0 0  0
9  1 0 0 1  1
10  1 0 1 0  1
11  1 0 1 1  0
12  1 1 0 0  0
13  1 1 0 1  1
14  1 1 1 0  1
15  1 1 1 1  0

#### cahlucas

Joined Dec 16, 2019
5
Part of it has been dropped due to an error. It should have said:
The examples may be presented in this form (see truth table below): X {A, B, C, D} = Σ {2,4,5,6,9,10,13,14}, with the solution: CD '+ A'BC' + AC'D (C AND (NOT D) OR (NOT A) AND B AND (NOT C) OR A AND (NOT C) AND D).

#### ci139

Joined Jul 11, 2016
1,696
(for this forum engine) can be done using the math add on
$\begin{array}{c|c|c|c|c|c} \unicode{32} & \mathbf{C} & \mathbf{C} & \mathbf{\overline{C}} & \mathbf{\overline{C}} & \unicode{32}\\ \hline \mathbf{A} & 0 & 1 & 1 & 0 & \mathbf{B}\\ \hline \mathbf{A} & 0 & 1 & 1 & 0 & \mathbf{\overline{B}}\\ \hline \mathbf{\overline{A}} & 0 & 1 & 1 & 1 & \mathbf{B}\\ \hline \mathbf{\overline{A}} & 0 & 1 & 0 & 0 & \mathbf{\overline{B}}\\ \hline \unicode{32} & \mathbf{D} & \mathbf{\overline{D}} & \mathbf{D} & \mathbf{\overline{D}} & \unicode{32} \end{array}\qquad {obviously \ X=C\overline{D}+A\overline{C}D+\overline{A}B\overline{C}\\ or \ X=\overline{CD+A\ \overline{C}\ \overline{D}+\overline{A}\ \overline{B}\ \overline{C}}=\\ =\overline{CD}·\overline{A\ \overline{C}\ \overline{D}}·\overline{\overline{A}\ \overline{B}\ \overline{C}}=\\ =\left({\overline{C}+\overline{D}}\right)\left({\overline{A}+C+D}\right)\left({A+B+C}\right)=\\ =...=\\ =C\overline{D}+A\overline{C}D+B\left({\overline{A}\ \overline{C}+C\oplus D}\right)}$
generated by the following :
Code:
$\begin{array}{c|c|c|c|c|c} \unicode{32} & \mathbf{C} & \mathbf{C} & \mathbf{\overline{C}} & \mathbf{\overline{C}} & \unicode{32}\\ \hline \mathbf{A} & 0 & 1 & 1 & 0 & \mathbf{B}\\ \hline \mathbf{A} & 0 & 1 & 1 & 0 & \mathbf{\overline{B}}\\ \hline \mathbf{\overline{A}} & 0 & 1 & 1 & 1 & \mathbf{B}\\ \hline \mathbf{\overline{A}} & 0 & 1 & 0 & 0 & \mathbf{\overline{B}}\\ \hline \unicode{32} & \mathbf{D} & \mathbf{\overline{D}} & \mathbf{D} & \mathbf{\overline{D}} & \unicode{32} \end{array}\qquad {obviously \ X=C\overline{D}+A\overline{C}D+\overline{A}B\overline{C}\\ or \ X=\overline{CD+A\ \overline{C}\ \overline{D}+\overline{A}\ \overline{B}\ \overline{C}}=\\ =\overline{CD}·\overline{A\ \overline{C}\ \overline{D}}·\overline{\overline{A}\ \overline{B}\ \overline{C}}=\\ =\left({\overline{C}+\overline{D}}\right)\left({\overline{A}+C+D}\right)\left({A+B+C}\right)=\\ =...=\\ =C\overline{D}+A\overline{C}D+B\left({\overline{A}\ \overline{C}+C\oplus D}\right)}$

Last edited:

#### cahlucas

Joined Dec 16, 2019
5
This is not what I had in mind... I need examples to test my program, and in order to do that, I will need some problems that are allready solved, so I can compare it to the output of my program.

#### ci139

Joined Jul 11, 2016
1,696
i realized that - but cryptic Boolean equations are better read in non-cryptic form (just a one time tutorial)

#### andrewmm

Joined Feb 25, 2011
632
Would this help,

you "prove" that two equations are the same , by either mathematical means , or putting all the combinations into the front of both and checking both outputs are the same.

Languages such as Modelsim are aimed at such simulations.

#### cahlucas

Joined Dec 16, 2019
5
Dear Mr. Andrewmm,
Where can I find this Modelsim? Sincerely, Karel.

#### ci139

Joined Jul 11, 2016
1,696

#### andrewmm

Joined Feb 25, 2011
632
Dear Mr. Andrewmm,
Where can I find this Modelsim? Sincerely, Karel.
try a search using your favourite search engine for "modelsim"

also have look at languages designed for logic description such as VHDL, and companies such as Xilinx, using the free version of vivado.