Sequential logic and implementation

Digital systems are used in vast variety of industrial applications and house hold electronic gadgets. Many of these digital circuits generate an output that is not only dependent on the current input but also some previously saved information which is used by the digital circuit. Consider the example of a digital counter which is used by many digital applications where a count value or the time of the day has to be displayed. The digital counter which counts downwards from 10 to 0 is initialized to the value 10. When the counter receives an external signal in the form of a pulse the counter decrements the count value to 9. On receiving successive pulses the counter decrements the currently stored count value by one, until the counter has been decremented to 0. On reaching the count value zero, the counter could switch off a washing machine, a microwave oven or switch on an air-conditioning system.

The counter stores or remembers the previous count value. The new count value is determined by the previously stored count value and the new input which it receives in the form of a pulse (a binary 1). The diagram of the counter circuit is shown in the figure.

Digital circuits that generate a new output on the basis of some previously stored information and the new input are known as Sequential circuits. Sequential circuits are a combination of Combinational circuits and a memory element which is able to store some previous information. Sequential circuits are a very important part of digital systems. Most digital systems have sequential logic in addition to the combinational logic. An example of sequential circuits is counters such as the down-counter which generates a new decremented output value based on the previous stored value and an external input. The storage element or the memory element which is an essential part of a sequential circuit is implemented a flip-flop using a very simple digital circuit known as a flip-flop.

Combinational Logic Circuits and Functional Devices

The logic gates which form the basic building blocks of a digital system are designed to perform simple logic operations. A single logic gate is not of much use unless it is connected with other gates to collectively act upon the input data. Different gates are combined to build a circuit that is capable of performing some useful operation like adding three numbers. Such circuits are known as Combinational Logic Circuits or Combinational Circuits. An Adder Combinational Circuit that is able to add two single bit binary numbers and give a single bit Sum and Carry output is shown. Figure 1.7.

Implementing large digital system by connecting together logic gates is very tedious and time consuming; the circuit implemented occupies large space, are power hungry, slow and are difficult to troubleshoot.

Digital circuits to perform specific functions are available as Integrated Circuits for use. Implementing a Digital system in terms of these dedicated functional units makes the system more economical and reliable. Thus an adder circuit does not have to be implemented by connecting various gates, a standard Adder IC is available that can be readily used. Other commonly used combinational functional devices are Comparators, Decoders, Encoders, Multiplexers and Demultiplexers.

Digital Components and their internal working

Digital system process binary information electronically through specialized circuits designed for handling digital information. These circuits as mentioned earlier operate with two voltage values of +5 volts and 0 volts. These specialized electronic circuits are known as Logic Gates and are considered to be the Basic Building Blocks of any Digital circuit.

The commonly used Logic Gates are the AND gate, the OR gate and the Inverter or NOT Gate. Other gates that are frequently used include NOR, NAND, XOR and XNOR. Each of these gates is designed to perform a unique operation on the input information which is known as a logical or Boolean operation.

Large and complex digital system such as a computer is built using combinations of these basic Logic Gates. These basic building blocks are available in the form of Integrated Circuit or ICs. These gates are implemented using standard CMOS and TTL technologies that determine the operational characteristics of the gates such as the power dissipation, operational voltages (3.3v or 5 v), frequency response etc.

Information Processing by a Digital System

A Digital system such as a computer not only handles numbers but all kinds of information.

• Numbers: A computer is able to store and process all types of numbers, integers, fractions etc. and is able to perform different kinds of arithmetic operations on the numbers.

• Text: A computer in a news reporting room is used to write and edit news reports. A Mathematician uses a computer to write mathematical equations explaining the dissipation of heat by a heat sink. The computer is able to store and process text and symbols.

• Drawings, Diagrams and Pictures: A computer can store very conveniently complex engineering drawings and diagrams. It allows real life still pictures or videos to be processed and edited.

• Music and Sound: Musicians and Composers uses a computer to work on a new compositions. Computers understand spoken commands. A Digital System (computer) is capable of handling different types of information, which is represented in the form of Binary Numbers. The different types of information use different standards and binary formats. For example, computers use the Binary number system to represent numbers. Characters used in writing text are represented through yet another standard known as ASCII which allows alphabets, punctuation marks and numbers to be represented through a combination of 0s and 1s.

Advantages of working in the Digital Domain

Handling information digitally offers several advantages. Some of the merits of a digital system are spelled out. Details of some these aspects will be discussed and studied in the Digital Logic Design course. Other aspects will be covered in several other courses.

• Storing and processing data in the digital domain is more efficient: Computers are very efficient in processing massive amounts of information and data. Computers process information that is represented digitally in the form of Binary Numbers. A Digital CD stores large number of video and audio clips. Sam number of audio and video clips if stored in analogue form will require a number of video and audio cassettes.

• Transmission of data in the digital form is more efficient and reliable: Modern information transmission techniques are relying more on digital transmission due to its reliability as it is less prone to errors. Even if errors occur during the transmission methods exist which allow for quick detection and correction of errors.

• Detecting and Correcting errors in digital data is easier: Coding Theory is an area which deals with implementing digital codes that allow for detection and correction of multi-bit errors. In the Digital Logic Design course a simple method to detect single bit errors using the Parity bit will be considered.
• Data can be easily and precisely reproduced: The picture quality and the sound quality of digital videos are far more superior to those of analogue videos. The reason being that the digital video stored as digital numbers can be exactly reproduced where as analogue video is stored as a continuous signal can not be reproduced with exact precision.

• Digital systems are easy to design and implement: Digital Systems are based on two-state Binary Number System. Consequently the Digital Circuitry is based on the two-voltage states, performing very simple operations. Complex Microprocessors are implemented using simple digital circuits. Several simple Digital Systems will be discussed in the Digital Logic course.

• Digital circuits occupy small space: Digital circuits are based on two logical states. Electronic circuitry that implements the two states is very simple. Due to the simplicity of the circuitry it can be easily implemented in a very small area. The PC motherboard having an area of approximately 1 sq.ft has most of the circuitry of a powerful computer. A memory chip small enough to be held in the palm of a hand is able to store an entire collection of books.

Binary Number System

The Binary Number System unlike the Decimal number system is based on two values. Each digit or bit in Binary Number system can represent only two values, a ‘0’ and a ‘1’. A single digit of the Decimal Number system represents 10 values, 0, 1, 2 to 9. The Binary Number System can be used to represent more than two values by combining binary digits or bits. In a Decimal Number System a single digit can represent 10 different values (0 to 9), representing more than 10 values requires a combination of two digits which allows up to 100 values to be represented (0 to 99). A Combination of Binary Numbers is used to represent different quantities.

• Represent Colours: A palette of four colours red, blue, green and yellow can be represented by a combination of two digital values 00, 01, 10 and 11 respectively.

• Representing Temperature: An analogue value such as 39oC can be represented in a digital format by a combination of 0s and 1s. Thus 39 is 100111 in digital form.

Any quantity such as the intensity of light, temperature, velocity, colour etc. can be represented through digital values. The number of digits (0s and 1s) that represents a quantity is proportional to the range of values that are to be represented. For example, to represent a palette of eight colours a combination of three digits is used. Representing a temperature range of 00 C to 1000 C requires a combination of up to seven digits.

Digital Systems uses the Binary Number System to represent two or multiple values, stores and processes the binary values in terms of 5 volts and 0 volts. Thus the number 39 represented in binary as 100111 is stored electronically in as +5 v, 0v, 0v, +5
v, +5 v and +5 v.

Digital Systems and Digital Values

Digital systems are designed to work with two voltage values. A +5 volts represents a logic high state or logic 1 state and 0 volts represents a logic low state or logic 0 state. The Digital Systems which are based on two voltage values or two states can easily represent any two values. For example,

• The numbers ‘0’ and ‘1’
• The state of a switch ‘on’ or ‘off’
• The colour ‘black’ and ‘white’
• The temperature ‘hot’ and ‘cold’
• An object ‘moving’ or ‘stationary’

Representing two values or two states is not very practical, as many naturally occurring phenomenons have values or state that are more than two. For example, numbers have widely varying ranges, a colour palette might have 64 different shades of the colour red, the temperature of boiling water at room temperature varies from 30 0C to 100 0C. Digital Systems are based on the Binary Number system which allows more than two or multiple values to be represented very conveniently.