Overview of Digital Circuits

A digital circuit is constructed of a power supply, devices, and conduction nets. Some nets provide circuit inputs from the “outside world”; in a schematic, these input nets are generally shown entering the left side of component and/or the overall circuit.

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Zeros and Ones

Information Representation in Digital Systems

A signal in a digital circuit is a circuit net that transports an output voltage from one device to one or more input connections of other devices. In a digital circuit, signals are constrained to be at one of two voltages, either Vdd or GND. Thus, all data in digital circuits are represented by signals that can be in one of only two states, and all data operations combine two-state data inputs to produce two-state data outputs.

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Basic Logic Functions and Truth Tables

A digital circuit represents and manipulates information encoded as electric signals that can assume one of two voltages: logic high (Vdd) or logic low (GND). Here we will dig further into the workings of digital circuits now that you have a better foundation for understanding.

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Transistors as Switches

Digital electronic circuits are built from electronic switches that are called transistors instead of the mechanical switches and resistors, as discussed in the previous sections. The basic concept is the same—the switches (transistors) are arranged so that they can be turned on or off by signals carrying either LLV or LHV.

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Introduction to CMOS Technology

Logic Circuits Built from FETs

Armed with the basic understanding of FET operation as described in previous sections, it is possible to construct a basic logic circuit that forms the back bone of all digital and computer circuits. These logic circuits will combine one or more input signals to produce an output signal according to the logic function requirements.

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Introduction to Combinational Logic Circuits

Behavior Definition and Schematic Representation

Combinational logic circuits use networks of logic gates to produce outputs that change in strict relation to input changes; that is, an output can only change state immediately after an input changes state.

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Product of Summation and Summation of Product

The terms “product” and “sum” have been borrowed from mathematics to describe AND and OR logic operations. Any logic system can be represented in one of these two logic ways.

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The XOR function is frequently used in digital circuits to manipulate signals that represent binary numbers.

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Logic Minimization

Efficiency of Different Implementations of Same Logic Functions

A digital logic circuit consists of a collection of logic gates; the input signals that drive them, and the output signals they produce. The behavioral requirements of a logic circuit are best expressed through truth tables or logic equations, and any design problem that can be addressed with a logic circuit can be expressed in one of these forms.

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Logic Minimization

Boolean Algebra

Boolean algebra is perhaps the oldest method used to minimize logic equations. It provides a formal algebraic system to manipulate logic equations so that the minimum can be found. A basic understanding of this system is indispensable to the study and analysis of logic circuits.

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Logic Minimization

Introduction to K-maps

Truth tables are not very useful for minimizing logic systems, and Boolean algebra has limited utility. Logic graphs offer the easiest and most useful pen-and-paper method of minimizing a logic system.

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Logic Minimization

K-maps with Don't Cares

Situations can arise where a circuit has N input signals, but not all 2N combinations of inputs are possible. Or, if all 2N combinations of inputs are possible, some combinations might be irrelevant.

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Logic Minimization

K-maps with Entered Variables

Entered variable maps simplify the process further by visually minimizing a K-map. The compression of the map makes a multi-variable system much easier to visualize and minimize.

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Logic Minimization

Multiple Outputs

Circuits that have more complex inputs and outputs then we have previously discussed require less tedious and error prone methods of analysis. Here we will discuss how multiple output systems are analyzed.

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Logic Minimization

Computer Based Logic Minimum

This page will introduce the two major algorithms used to analyze and minimize logic systems. Both are still valid and used algorithms, however, one is more widely used then the other.

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Resistance and Ohm's Law

In 1827, George Ohm demonstrated through a series of experiments that voltage, current, and resistance are related through a fundamental relationship: Voltage (V) is equal to Current (I) times resistance (R).

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Program FPGA using Xilinx® iMPACT™

This page demonstrates how to properly program an FPGA using Xilinx® iMPACT™.

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Introduction to Electronic Circuits

Real Digital Project 1

This project presents a brief, non-rigorous introduction to electronic circuits and systems. Only the most essential concepts are presented, with emphasis on topics used in later projects. As with all projects in this module, a companion “Exercise1” document is available for further understanding.

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Introduction to Digilent FPGA-based Boards

Real Digital Project 2

This project introduces Digilent’s FPGA-based circuit boards and the Adept™ software that is used to program them. In tutorial fashion, Adept is used to download a logic circuit to the board, and that circuit is used in an experiment with basic logic circuits.

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Logic Circuit Structure with an Introduction to Computer Aided Design (CAD) tools

Real Digital Project 3

This module presents the basic structure of combinational logic circuits, and introduces the use of computer aided design (CAD) tools in modern circuit design.

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Logic Minimization

Real Digital Project 4

The requirements for new logic circuit designs are often expressed in some loose, informal manner. For an informal behavioral description to result in an efficient, well designed circuit that meets the stated requirements, appropriate engineering design methods must be developed.

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Introduction to VHDL

Real Digital Project 5

Since the first widespread use of CAD tools in the early 1970's, circuit designers have used both picture-based schematic tools and text-based netlist tools. Schematic tools dominated the CAD market through the mid-1990's because using a graphics editor to build a structural picture of a circuit was easy compared to typing a detailed, error-free netlist.

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Combinational Circuit Blocks

Real Digital Project 6

This lab introduces several combinational circuits that are frequently used by digital designers, including a data selector (also called a multiplexor or just "mux"), a binary decoder, a seven-segment decoder, an encoder, and a shifter.

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Combinational Arithmetic Circuits

Real Digital Project 7

This project examines several combinational circuits that perform arithmetic operations on binary numbers, including adders, subtractors, multipliers, and comparators.

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