A term is a collection of variables, e.g. ABCD.
A constant is a value or quantity which has a fixed meaning. In
conventional algebra the constants include all integers and
fractions. In Boolean algebra there are only two possible
constants, one and zero. These two constants are used to describe
true and false, up and down, go and not go etc.
A variable is a quantity which changes by taking on the value of
any constant in the algebraic system. At any one time the
variable has a particular value of constant. There are only two
values of constants in the system- therefore a variable can only
be zero or one. Variables are denoted by letters.
A literal is a variable or its complement
Also known as the standard product or canonic product term. This is
a term such as , etc., where each variable
is used once and once only.
Also known as the standard sum or canonic sum term. This is a term
such as , etc., where each variable is
used once and once only.
Also known as the minterm canonic form or canonic sum function.
A function in the form of the " sum " (OR) of minterms, e.g:
Also known as the maxterm canonic form or canonic product function. A function in the
form of the " product " (AND) of maxterms, e.g:
Also known as the normal sum function. A function in the form of the " sum "
of normal product terms, e.g:
Also known as the normal product function. A function in the form of the " product "
of normal sum terms, e.g:
A term such as etc.
A term such as etc.
The name "truth table" comes from a similar table used in
symbolic logic, in which the truth or falsity of a statement is
listed for all possible proposition conditions. The truth table
consists of two parts; one part comparising all combinations of
values of the variables in a statement (or algebraic expression),
the other part containing the values of the statement for each
combination. The truth table is useful in that it can be used to
verify Boolean identities.
Consider the following map. The function plotted is
Using algebraic simplification, by using T9a of the Boolean Laws (A + = 1).
Referring to the map we can encircle the adjacent cells and infer that A and are not required.
If two occupied cells of a Karnaugh are adjacent, horizontally or vertically (but not diagonally)
then one variable is redundant. This has resulted by labelling the map as shown,
i.e. adjacent cells satisfy the condition A + = 1.
It is an implicant of a function which does not imply any other implicant of the function.
The chart is used to remove redundant prime implicants. A grid is prepared having all the
prime implicants listed down the left and all the minterms of the function along the top.
Each minterm covered by a given prime implicant is marked in the appropiate postion.
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Composed by David Belton - April 98