*Glossary*

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*