Digital Circuits Basic Concept

Digital circuits

Digital circuits process and manipulate binary signals, performing logical and arithmetic operations.

They are essential in computing and electronic devices for information storage, computation, and signal control.

Digital circuits are basically divided into two major categories: Combinational circuits and Sequential circuits.

Combinational Circuits

A combinational circuits is a types of circuit that the output is dependent of the present values of the input variables but independent of the previous values. There is no effect of previous inputs on the present outputs, because these circuits have no memory.

Such as: Adders, Encoder, Decoder, Multiplexers, De-Multiplexers, Comparators, and Arithmetic Logic Unit.

Sequential Circuits

The sequential circuit is a special type of circuit that has a series of inputs and outputs.
The outputs of the sequential circuits depend on both the combination of present inputs and previous outputs. The previous output is treated as the present state. So, the sequential circuit contains the combinational circuit and its memory storage elements. A sequential circuit doesn’t need to always contain a combinational circuit.

Such as: Flip-Flops, Shift Registers, Counters, Memory Units, State Machines, and Clock Dividers.

In sequential circuits the current state of the output is dependent not only on the current inputs but also on past inputs/outputs. That is, there must be some memory elements for storing past information.

Sequential circuits can be further divided into two types: Asynchronous and Synchronous.

Asynchronous

In asynchronous circuits the output is independent of clocking. That is, it can change its output states without waiting for a clock pulse.

Synchronous

In synchronous circuits, the outputs are allowed to change states in synchronism with a clock signal. That is, the time at which the outputs can change states is determined by a clock signal.

Synchronous circuits are comparatively easier to design and troubleshoot than asynchronous circuits.

Difference between the combinational circuits and sequential circuits

1. The outputs of the combinational circuit depend only on the present inputs.
1. The outputs of the sequential circuits depend on both present inputs and previous output.

2. The feedback path is not present in the combinational circuit.
2. The feedback path is present in the sequential circuits.

3. In combinational circuits, memory elements are not required.
3. In the sequential circuit, memory elements are important role and required.

4. The clock signal is not required for combinational circuits.
4. The clock signal is required for sequential circuits.

5. The combinational circuit is simple to design.
5. The sequential circuit is not just simple design.

Adder

The electronic circuit that is designed to perform the addition of two or more numbers, more specifically binary numbers, is known as an adder.
As we know, logic circuits use a binary number system to perform the operations, hence the adder is also referred to as a binary adder.

Half Adder
Half adder is a combinational logic circuit that is designed to add two binary digits. The half adder provides the output along with a carry (if any).

The half adder circuit can be designed by connecting an XOR gate and one AND gate.

Full Adder
A full adder is also a combinational logic circuit that can add two binary digits (bits) and a carry bit and produces a sum bit and a carry bit as output.
In other words, a combinational circuit which is designed to add three binary digits and produces two outputs (sum and carry) is known as a full adder.
Thus, a full adder circuit adds three binary digits, where two are the inputs and one is the carry forwarded from the previous addition.

Encoder
An encoder is a device that converts a physical signal into a digital signal.

The encoder is also a combinational logic circuit; it converts information, such as a decimal number or an alphabetic character, into some coded form such as binary or BCD.

Encoders are used in a variety of applications, such as robotics, industrial control, and telecommunications.

Decoder
A decoder is a device, circuit, or program that converts an analogue signal into digital data.
It is a types of Multiple Input & Multiple Output device.
Decoder is a combinational circuit that converts n lines of input into maximum 2^n lines of output.

• Applications of decoders are converting binary code to other codes like:
• Binary to octal
• Binary to Hexadecimal
• Binary to decimal

Multiplexers
Multiplexer is a combinational circuit that has maximum of 2 data inputs, ‘n’ selection lines and single output line. One of these data inputs will be connected to the output based on the values of selection lines.
Since there are ‘n’ selection lines, there will be 2 possible combinations of zeros and ones.
So, each combination will select only one data input. Multiplexer is also called as Mux.

De-Multiplexers
De-Multiplexer is a combinational circuit that performs the reverse operation of Multiplexer. It has single input, ‘n’ selection lines and maximum of 2 outputs. The input will be connected to one of these outputs based on the values of selection lines.
Since there are ‘n’ selection lines, there will be 2 possible combinations of zeros and ones.
So, each combination can select only one output. De-Multiplexer is also called as De-Mux.

Comparators

A comparator is a combinational circuit that takes two binary numbers as input and determines the relationship between them.

The output of a comparator indicates whether the numbers are equal, and if not, which one is greater or lesser. Comparators are commonly used in digital systems for tasks such as decision-making, sorting, and control logic.

Arithmetic Logic Unit

An Arithmetic Logic Unit (ALU) is a crucial component of a central processing unit (CPU) in a computer.

It is a combinational circuit that performs arithmetic and logical operations on binary numbers.

The ALU takes two binary inputs, performs a specified operation, and produces a binary output along with some status flags.

Flip-Flops

The memory element that is used in sequential circuits is called flip-flop.

Flip-flop is a sequential logical circuit, which is an edge trigger or sensitive. The flip-flop and latch are made via different logic gates. Flip-flop is different from latch because the clock feature is not present in latches, which is important for Flip-flop operations. The output of Flip-flops will change either at the increasing edge or decreasing edge of the clock pulse, whereas the output is a change in the latch at the change of the level of clock pulse either
high or low level.

A flip-flop can store only one bit of information. It consists of some logic gates. Though a logic gate has no storage capacity of its own, several gates can be connected together in such a way that permit information to be stored.

The most basic flip-flop circuit can be constructed using either two cross-coupled NAND gates (known as NAND latch) or two cross-coupled NOR gates (known as NOR latch).

One latch or flip-flop can store only 1-bit of information.

The main difference between latches and flip-flops is that the outputs of latches are constantly affected by their inputs as long as the enable signal is asserted.

On the other hand, for flip-flops, the outputs change only either at the rising or falling edge of the enable signal (clock signal). The outputs of the flip-flops remain unchanged after the rising or falling edge of the clock, even if the inputs change.

Shift Registers

Flip-flop is a 1 bit memory cell which can be used for storing the digital data. To increase the storage capacity in terms of number of bits, we have to use a group of flip flop. Such a group of flip-flop is known as a Register.

The n-bit register will consist of n number of flip-flop and it is capable of storing an n-bit word.

The binary data in a register can be moved within the register from one flip-flop to another. The registers that allow such data transfers are called as shift registers.

There are four mode of operations of a shift register.
 Serial Input Serial Output
 Serial Input Parallel Output
 Parallel Input Serial Output
 Parallel Input Parallel Output

Counters

Counters are a type of sequential circuit that generate a sequence of binary numbers in response to clock pulses. They are widely used in digital systems for applications such as counting events, generating timing signals, and controlling sequential processes. Counters can be categorized into two main types: synchronous counters and asynchronous counters.

Memory Units

Memory units in sequential circuits are components that store and retrieve digital information.

Unlike combinational circuits, which have no inherent memory, sequential circuits incorporate memory elements to retain information about past inputs or states.

Memory units are crucial in applications where storing and recalling data is necessary, such as in computer systems, microcontrollers, and various digital devices.

State Machines

State machines are a type of sequential circuit used to model and control systems that exhibit different states in response to input stimuli. State machines consist of a set of states, transitions between these states, and actions associated with transitions. They are widely employed in digital systems for tasks such as control logic, protocol implementation, and sequencing operations. There are two main types of state machines: Mealy machines and Moore machines.

Clock Dividers

Clock dividers are sequential circuits designed to divide the frequency of an input clock signal to produce a lower-frequency output signal.

These dividers are widely used in digital systems to generate clock signals of different frequencies for various components, allowing for synchronization and control of different parts of the system.

Clock dividers can be implemented using different types of sequential circuits, such as flip-flops and counters.

 

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