Input a boolean expression into the Expression field, e.g.
if x then y
could be inputted as
x => y
, or it could be inputted as
x' + y (not x or y)
Normally, it is assumed that the boolean expression is equated to 1⁄True. So if you input
yz + a'x' + a'z' + xy
, the program interprets this as
yz + a'x' + a'z' + xy = 1
If you want to input a boolean expression which is equated to 0, surround the expression with parentheses, and append an apostrophe at the end.
Or just write it as <expression> = 0.
So for example, if you want to analyze the expression ABC + ACD + AB'D + A'BC' + BC'D = 0, then input either
ABC + ACD + AB'D + A'BC' + BC'D = 0
(ABC + ACD + AB'D + A'BC' + BC'D)'
After inputting your expression, click the Generate button. After processing and displaying the boolean⁄fourier attributes, it will populate the variable listbox, near the bottom left, under Solve Boolean Equation. This listbox will be populated with all of the variable letters from the Boolean Expression. To solve for any of the variables, simply select the variable, and wait for processing to complete.
Some valid Boolean expressions are
((S + yR'T' + y'T) = Y)(RS + RT +ST)'
(yz + a'x' + a'z' + xy)'
BX = C
PORETSKY's Law of Forms
(For more information, see
Boolean Reasoning, by Frank Markham Brown, Second Edition, Section 5.5, Poretsky's Law of Forms,
The Algebra of Logic, by Louis Coutarat, 1914, Section 0.43 The Law of Forms
A Survey of Symbolic Logic, Clarence Irving Lewis, 1918, p. 145, section 7.15
To solve h for an equation g = h <==> f = 0,
Input the ZERO form of the expression f, into the Expression field. Then click the Generate button, to obtain the Prime Implicants and Minimized expression. Also, input the ZERO form of the expression h, into the Poretsky Form to Solve field, and then click Solve.
Using the example from Boolean Reasoning, Section 5.5, the author starts with the expression
xy' + z = 0 (Here, we are using x to represent the author's x(1); y to stand for x(2); and z to stand for x(3).)
, so the user will want to input either
xy' + z = 0
(xy' + z)' into the Expression field, and click Generate.
The author then requests the user to solve for g, when g = yz, if and only if xy' + z = 0,
, so the user should input
yz = 0
In the Poretsky Form to Solve field, and click Solve. The answer, y'( x + z ) (equivalently, y'x + y'z) should match the author's answer, at the end of Section 5.5.