DE 2.1 & 2.2

DeMorgan's Theorems

1) Theorem stating that the complement of a sum (OR operation) equals the product (AND operation) of the complements, and

Logic Diagram

A diagram, similar to a schematic, showing the connection of logic gates.

Karnaugh Map

A graphical tool for finding the maximum SOP or POS simplification of a Boolean expression. A Karnaugh map works by arranging the terms of an expression so that variable scans are cancelled by grouping minterms or maxterms.

Truth Table

A list of all possible input values to a digital circuit, listed in ascending binary order, and the output response for each input combination.

Associative Property

A mathematical function is associative if its operands can be grouped in any order without affecting the result. For example, addition is associative ((a+b) + c = a + (b+c)), but subtraction is not ((a-b) -c ≠ a-(b-c)).

Commutative Property

A mathematical operation is commutative if it can be applied to its operands in any order without affecting the result. For example, addition is commutative (a+b=b+a), but subtraction is not (a-b≠b-a).

Binary Number System

A number system used extensively in digital systems, based on the number 2. It uses two digits to write any number.

Minterm

A product term in a Boolean expression where all possible variables appear once in true or complement form.

Maxterm

A sum term in a Boolean expression where all possible variables appear once in true or complement form.

Product Term

A term in a Boolean expression where one or more true or complement variables are ANDed.

Sum Term

A term in a Boolean expression where one or more true or complement variables are ORed.

Sum-of-Products (SOP)

A type of Boolean expression where several product terms are summed (ORed) together.

Product-of-Sums (POS)

A type of Boolean expression where several sum terms are multiplied (ANDed) together.

Boolean Variable

A variable having only two possible values, such as HIGH/LOW, 1/0, On/Off, or True/False.

Boolean Algebra

Algebraic process used as a tool in the design and analysis of digital systems. In Boolean algebra only two values are possible, 0 and 1.

Boolean Expression

An algebraic expression made up of Boolean variables and operators, such as AND (), OR (+), or NOT (-). Also referred to as Boolean function or a logic function.

Logic Circuit

Any circuit that behaves according to a set of logic rules.

Combinational Logic

Digital circuitry in which an output is derived from the combination of inputs, independent of the order in which they are applied.

Distributive Property

Full name: distributive property of multiplication over addition. The property that allows us to distribute ("multiply through") an AND across several OR functions. For example, a(b+c)=ab+ac.

NAND Gate

Logic circuit that operates like an AND gate followed by an INVERTER.

NOR Gate

Logic circuit that operates like an OR gate followed by an INVERTER.

Decimal System

Number system that uses 10 different digits or symbols to represent a quantity.

Boolean Theorems

Rules that can be applied to Boolean algebra to simplify logic expressions.

Don't Care Condition

Situation when a circuit's output level for a given set of input conditions can be assigned as either a 1 or 0.

Most Significant Bit (MSB)

The leftmost bit in a binary number. This bit has the number's loargest positional multiplier.

Least Significant Bit (LSB)

The rightmost bit of a binary number. This bit has the number's smallest positional multiplier.

Cell

The smallest unit of Karnaugh map, corresponding to one line of a truth table. The input variables are the cell's coordinates and the output variable is the cell's contents.

Adjacent Cell

Two cells in a K-map are adjacent if there is only one variable that is different between the coordinates of the two cells.