Digital Electronics 2

Combinational Logic

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)).

Binary Number System

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

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.

Boolean Theorems

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

Boolean Variable

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

Combinational Logic

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

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).

Decimal System

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

DeMorgan's Theorems

\[1] The complement of a sum (OR operation) equals the product (AND operation) of the complements, and [2] The complement of a product (AND operation) equals the sum (OR operation) of the complements.

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.

Least Significant Bit (LSB)

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

Logic Circuit

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

Logic Diagram

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

Maxterm

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

Minterm

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

Most Significant Bit (MSB)

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

Product-of-Sums (POS)

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

Product Term

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

Sum-of-Products (SOP)

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

Sum Term

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

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.

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.

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.

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.

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.

NAND Gate

Logic circuit that operates like an AND gate followed by an INVERTER. The output of a NAND gate is LOW (logic level 0) only if all inputs are HIGH (logic level 1).

NOR Gate

Logic circuit that operates like an OR gate followed by an INVERTER. The output of a NOR gate is LOW (logic level 0) when any or all inputs are HIGH (logic level 1).

Common Anode Display

A seven-segment LED display where the anodes of all the LEDs are connected to the circuit supply voltage. Each segment is illuminated by a logic LOW at its cathode.

Common Cathode Display

A seven-segment display in which the cathodes of all the LEDs are connected together and grounded. A logic HIGH illuminates a segment when applied to its anode.

Datasheet

A printed specification giving details of the pin configuration, electrical properties, and mechanical profile of an electronic device.

Design Specifications

A detailed description, especially one providing information needed to make, build, or produce something.

Seven-Segment Display

An array of seven independently controlled light-emitting diodes (LED) or liquid crystal display (LCD) elements, shaped like a figure 8, which can be used to display decimal digits and other characters by turning on the appropriate elements.

De-multiplexer

A circuit that uses a binary decoder to direct a digital signal from a single source to one of several destinations.

Encoder

A digital circuit that produces an output code depending on which of its inputs is activated.

Exclusive-NOR (XNOR) Circuit

Two-input logic circuit that produces a high output only when the inputs are equal.

Exclusive-OR (XOR) Circuit

Two-input logic circuit that produces a high output only when the inputs are different.

Full Adder

Logic circuit with three inputs and two outputs. The inputs are a carry bit (CIN) from a previous stage, a bit from the augend, and a bit from the addend, respectively. The outputs are the sum bit and the carry-out bit (COUT) produced by the addition of the bit from the addend with the bit from the augend and CIN.

Half Adder

Logic circuit with two inputs and two outputs. The inputs are a bit from the augend and a bit from the addend. The outputs are the sum bit produced by the addition of the bit from the addend with the bit from the augend and the resulting carry (COUT) bit, which will be added to the next stage.

Hexadecimal Number System

Base-16 number system. Hexadecimal numbers are written with sixteen digits, 0-9 and A-F, with power-of-16 positional multipliers.

Multiplexer

A circuit that directs one of several digital signals to a single output, depending on the states of several select inputs.

Octal Number System

A number system that has a base of 8; digits from 0 to 7 are used to express an octal number.

Seven-Segment Display

An array of seven independently controlled light-emitting diodes (LED) or liquid crystal display (LCD) elements, shaped like a figure-8, which can be used to display decimal digits and other characters by turning on the appropriate elements.

Signed Binary Number

A binary number of fixed length whose sign is represented by one bit, usually the most significant bit, and whose magnitude is represented by the remaining bits.

Sign Bit

A binary bit that is added to the leftmost position of a binary number to indicate whether that number represents a positive or a negative quantity.

1's Complement

A form of signed binary notation in which negative numbers are created by complementing all bits of a number, including the sign bit.

2's Complement

A form of signed binary notation in which negative numbers are created by adding 1 to the 1's complement form of the number.

Complex PLD (CPLD)

A digital device consisting of several programmable sections with internal interconnections between the sections.

Compiler

The process used by CPLD design software to interpret design information (such as a schematic or text file) and create required programming information for a CPLD.

Design Entry

The process of using software tools to describe the design requirements of a PLD. Design entry can be done by entering a schematic or a text file that describes the required digital function.

Field Programmable Gate Array (FPGA)

Class of PLDs that contain an array of more complex logic cells that can be very flexibly interconnected to implement high-level logic circuits.

Fitting

Assigning internal PLD circuitry, and input and output pins, to a PLD design.

Integrated Circuit (IC)

An electronic circuit having many components, such as transistors, diodes, resistors, and capacitors, in a single package.

JTAG Port

A four-wire interface specified by the Joint Test Action Group (JTAG) used for loading test data or programming data into a PLD installed in a circuit.

JEDEC

Joint Electron Device Engineering Council.

JEDEC File

An industry standard form of text file indicating which fuses are blown and which are intact in a programmable logic device.

JTAG

Joint Test Action Group. A standards body that developed the format for testing and programming devices while they are installed in a system.

Programmable Logic Device (PLD)

Digital integrated circuit that can be programmed by the user to implement any digital logic function.

Programming

Transferring design information from the computer running PLD design software to the actual PLD chip.

Schematic Entry

A technique of entering CPLD design information by using a CAD (computer aided design) tool to draw a logic circuit as a schematic. The schematic can then be interpreted by design software to generate programming information for the CPLD.

Simple PLD (SPLD)

A PLD with a few hundred logic gates and possibly a few programmable macrocells available.

Target Device

The specific PLD for which a digital design is intended.

TCK

Test Clock. The JTAG signal that drives the JTAG downloading process from one state to the next.

TDI

Test Data In. In a JTAG port, the serial input data to a device.

TDO

Test Data Out. In a JTAG port, the serial output data from a device.

TMS

Test Mode Select. The JTAG signal that controls the downloading of test or programming data.