# Glossary

### Term

A term is a collection of variables, e.g. ABCD.

### Constant

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.

### Variable

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.

### Literal

A literal is a variable or its complement ### Minterm

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.

### Maxterm

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.

### Standard sum of products form

Also known as the minterm canonic form or canonic sum function. A function in the form of the " sum " (OR) of minterms, e.g: ### Standard product of sums form

Also known as the maxterm canonic form or canonic product function. A function in the form of the " product " (AND) of maxterms, e.g: ### Sum of products

Also known as the normal sum function. A function in the form of the " sum " of normal product terms, e.g: ### Product of sums

Also known as the normal product function. A function in the form of the " product " of normal sum terms, e.g: ### Normal (general) sum term

A term such as etc.

### Normal (general) product term

A term such as etc.

### Truth table

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.

### Prime implicants

It is an implicant of a function which does not imply any other implicant of the function.

### Prime implicant chart

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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